Question 1

You are performing seven independent Bernoulli trials with $p = 0.8$ and $q = 0.2$ . Calculate the probability of three successes. Please, round the answer to four decimal places.

Accepted Answer

The answer of You are performing seven independent Bernoulli trials...

Question 2

You are performing 5 independent Bernoulli trials with $p = 0.6$ and $q = 0.4$ . Calculate the probability that it will be at most 2 successes. Round your answer to five decimal places if necessary.

Accepted Answer

The probability of at most 2 successes in 5 independent Bernoulli trials with $p = 0.6$ and $q = 0.4$ can be calculated using the binomial distribution formula: $P(X = k) = \binom{n}{k} p^k q^{(n-k)}$, where $n = 5$, $p = 0.6$, and $q = 0.4$. We calculate for $k = 0, 1, 2$ and sum these probabilities.For $k = 0$: $P(X = 0) = \binom{5}{0} (0.6)^0 (0.4)^5 = 0.01024$For $k = 1$: $P(X = 1) = \binom{5}{1} (0.6)^1 (0.4)^4 = 0.0768$For $k = 2$: $P(X = 2) = \binom{5}{2} (0.6)^2 (0.4)^3 = 0.2304$Summing these probabilities gives $0.01024 + 0.0768 + 0.2304 = 0.31744$.

Question 3

​Assume that on a standardized test of 100 questions, a person has a probability of 86% of answering any particular question correctly. Find the probability of answering between 75 and 85 questions, inclusive, correctly. (Assume independence, and round your answer to four decimal places.) ​

Accepted Answer

The answer of ​Assume that on a standardized test of...

Question 4

You are performing seven independent Bernoulli trials with $p = 0.1$ and $q = 0.9$ . Calculate the probability of no successes. Round your answer to four decimal places.

Accepted Answer

The answer of You are performing seven independent Bernoulli trials...

Question 5

X is a binomial variable with and $p = \frac { 1 } { 5 }$ . Compute the probability $P ( 0 < X < 2 )$ . Round your answer to four decimal places .

Accepted Answer

The answer of X is a binomial variable with and...

Question 6

X is a binomial variable with $n = 4$ and $p = \frac { 1 } { 2 }$ . Compute the probability correct to four decimal places $P ( 0 \leq X \leq 2 )$ .
​ $P ( 0 \leq X \leq 2 ) \approx$ __________

Accepted Answer

The answer of X is a binomial variable with \(n...

Question 7

In a large on-the-job training program, half of the participants are female and half are male. In a random sample of 6 participants, what is the probability that an investigator will draw at least 2 females  Round your answer to four decimal places.

Accepted Answer

We can use the binomial distribution to solve this problem.

Let X be the number of females in a sample of 6 participants. Then, X follows a binomial distribution with parameters n = 6 and p = 0.5 (since half of the participants are female).

We want to find P(X ≥ 2), which is the probability of drawing at least 2 females.

Using the binomial distribution formula or a calculator, we get:

P(X ≥ 2) = 1 - P(X < 2)
= 1 - P(X = 0) - P(X = 1)
= 1 - (0.5)⁶ - 6(0.5)⁵(0.5) - 15(0.5)⁴(0.5)²
= 0.890625

Therefore, the probability that an investigator will draw at least 2 females in a random sample of 6 participants is 0.8906 (rounded to four decimal places), which corresponds to choice B.

Question 8

X is a binomial variable with $n = 6$ and $p = 0.4$ . Compute $P ( X = 4 )$ . Round your answer to five decimal places.

Accepted Answer

The probability $P(X = 4)$ in a binomial distribution is calculated using the formula $P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$, where $n$ is the number of trials, $p$ is the probability of success on a single trial, and $k$ is the number of successes. Plugging in $n = 6$, $p = 0.4$, and $k = 4$, we get $P(X = 4) = \binom{6}{4} (0.4)^4 (0.6)^2 = 15 \times 0.0256 \times 0.36 = 0.13824$.

Question 9

According to a July, 1999, article in the New York Times, 13.5% of Internet stocks that entered the market in 1999 ended up trading below their initial offering prices. If you were an investor who purchased 11 Internet stocks at their initial offering prices, what was the probability that at least 10 of them would end up trading at or above their initial offering price  (Round your answer to four decimal places.) ?

Accepted Answer

The probability that a stock will not end up trading below its initial offering price is 1-0.135=0.865. 
Using the binomial distribution with n=11 and p=0.865, we can find the probability that at least 10 out of the 11 stocks will end up trading at or above their initial offering price.

P(X≥10) = 1 - P(X<10)
= 1 - [(P(X=0) + P(X=1) + ... + P(X=9)]
= 1 - 0.0117
= 0.9883

Rounded to four decimal places, the probability is 0.5511. So, the best choice is C.

Question 10

The probability that a randomly chosen citizen-entity of Cygnus is of pension age is approximately 0.6. What is the probability that, in a randomly selected sample of 3 citizen-entities, all of them are of pension age  Round your answer to four decimal places. ?

Accepted Answer

The probability of a citizen-entity being of pension age is 0.6. Therefore, the probability of all three being of pension age is $(0.6)^3=0.216$. Round to four decimal places, the answer is 0.216.

Question 11

According to a study, the probability that a randomly selected teenager watched a rented video at least once during a week was 0.78. What is the probability that at least 8 teenagers in a group of 10 watched a rented movie at least once last week  Express your answer to the nearest hundredth. ?

Accepted Answer

The probability of at least 8 teenagers watching a rented movie at least once last week is the complement of the probability that 7 or fewer teenagers watched a rented movie at least once last week. The probability that 7 or fewer teenagers watched a rented movie at least once last week is the sum of the probabilities that 0, 1, 2, 3, 4, 5, 6, or 7 teenagers watched a rented movie at least once last week. The probability that 0 teenagers watched a rented movie at least once last week is (1 - 0.78)^10 = 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Question 12

In a large on-the-job training program, half of the participants are female and half are male. In a random sample of 4 participants, what is the probability that an investigator will draw at least 1 male  Please, round your answer to four decimal places.

Accepted Answer

The probability of drawing at least 1 male in a sample of 4 participants, given that half of the participants are male and half are female, can be calculated by subtracting the probability of drawing no males (all females) from 1. The probability of drawing all females is (1/2)^4 = 1/16 = 0.0625. Therefore, the probability of drawing at least 1 male is 1 - 0.0625 = 0.9375.

Question 13

X is a binomial variable with $n = 6$ and $p = 0.4$ . Compute $P ( X = 5 )$ . Round your answer to four decimal places.
​ $P ( X = 5 ) =$ __________

Accepted Answer

The answer of X is a binomial variable with \(n...

Question 14

The probability that a randomly selected pound of beef is purchased by McDonald's is 0.09. Ten pounds of beef are chosen at random. What is the probability that exactly two of them are purchased by McDonald's  Round your answer to four decimal places.

Accepted Answer

This is a binomial probability problem where n = 10 (number of trials), k = 2 (number of successes), and p = 0.09 (probability of success on a single trial). The formula for binomial probability is P(X = k) = (n choose k) * p^k * (1-p)^(n-k). Plugging in the values: P(X = 2) = (10 choose 2) * (0.09)^2 * (0.91)^8 ≈ 0.1714.

Question 15

X is a binomial variable with $n = 7$ and $p = 0.4$ . Compute $P ( 1 \leq X \leq 3 )$ . Round your answer to four decimal places.
​ $P ( 1 \leq X \leq 3 ) =$ __________

Accepted Answer

The answer of X is a binomial variable with \(n...

Question 16

It is known that 69% of all the ZeroCal hamburger patties produced by your factory actually contain more than 1,000 calories. Compute the probability distribution for $n = 50$ Bernoulli trials. What is the most likely value for the number of burgers in a sample of 50 that contain more than 1,000 calories

Accepted Answer

The most likely value for a binomial distribution is the mode, which is given by $\lfloor (n+1)p \rfloor$. Here, $n = 50$ and $p = 0.69$, so $\lfloor (50+1) \times 0.69 \rfloor = \lfloor 35.19 \rfloor = 35$.

Question 17

Your manufacturing plant produces air bags, and it is known that 50% of them are defective. Fifteen air bags are tested. Find the probability that at least two of them are defective. Round your answer to four decimal places.

Accepted Answer

The answer of Your manufacturing plant produces air bags, and...

Question 18

You are performing 5 independent Bernoulli trials with $p = 0.2$ and $q = 0.8$ . Calculate the probability of 2 successes. Round your answer to five decimal places if necessary.

Accepted Answer

The probability of 2 successes in 5 trials is given by the binomial probability formula: $ P(X = 2) = \binom{5}{2} \times (0.2)^2 \times (0.8)^3 = 10 \times 0.04 \times 0.512 = 0.2048 $.

Question 19

You are performing five independent Bernoulli trials with $p = 0.1$ and $q = 0.9$ . Calculate the probability of no failures. Round your answer to four decimal places.

Accepted Answer

The answer of You are performing five independent Bernoulli trials...

Question 20

X is a binomial variable with $n = 6$ and $p = 0.6$ . Compute $P ( X \leq 2 )$ . Round your answer to five decimal places.

Accepted Answer

The probability $P(X \leq 2)$ in a binomial distribution with $n = 6$ and $p = 0.6$ can be calculated using the binomial probability formula for each of $X = 0, 1, 2$ and summing these probabilities. The correct calculation leads to $P(X \leq 2) = 0.1792$, making option C the correct answer.

Quiz 9: Random Variables and Statistics

You are performing seven independent Bernoulli trials with $p = 0.8$ and $q = 0.2$ . Calculate the probability of three successes. Please, round the answer to four decimal places.

You are performing 5 independent Bernoulli trials with $p = 0.6$ and $q = 0.4$ . Calculate the probability that it will be at most 2 successes. Round your answer to five decimal places if necessary.

Assume that on a standardized test of 100 questions, a person has a probability of 86% of answering any particular question correctly. Find the probability of answering between 75 and 85 questions, inclusive, correctly. (Assume independence, and round your answer to four decimal places.)

You are performing seven independent Bernoulli trials with $p = 0.1$ and $q = 0.9$ . Calculate the probability of no successes. Round your answer to four decimal places.

X is a binomial variable with and $p = \frac { 1 } { 5 }$ . Compute the probability $P ( 0 < X < 2 )$ . Round your answer to four decimal places .

X is a binomial variable with $n = 4$ and $p = \frac { 1 } { 2 }$ . Compute the probability correct to four decimal places $P ( 0 \leq X \leq 2 )$ . $P ( 0 \leq X \leq 2 ) \approx$ __________

In a large on-the-job training program, half of the participants are female and half are male. In a random sample of 6 participants, what is the probability that an investigator will draw at least 2 females Round your answer to four decimal places.

X is a binomial variable with $n = 6$ and $p = 0.4$ . Compute $P ( X = 4 )$ . Round your answer to five decimal places.

The probability that a randomly chosen citizen-entity of Cygnus is of pension age is approximately 0.6. What is the probability that, in a randomly selected sample of 3 citizen-entities, all of them are of pension age Round your answer to four decimal places. ?

According to a study, the probability that a randomly selected teenager watched a rented video at least once during a week was 0.78. What is the probability that at least 8 teenagers in a group of 10 watched a rented movie at least once last week Express your answer to the nearest hundredth. ?

In a large on-the-job training program, half of the participants are female and half are male. In a random sample of 4 participants, what is the probability that an investigator will draw at least 1 male Please, round your answer to four decimal places.

X is a binomial variable with $n = 6$ and $p = 0.4$ . Compute $P ( X = 5 )$ . Round your answer to four decimal places. $P ( X = 5 ) =$ __________

The probability that a randomly selected pound of beef is purchased by McDonald's is 0.09. Ten pounds of beef are chosen at random. What is the probability that exactly two of them are purchased by McDonald's Round your answer to four decimal places.

X is a binomial variable with $n = 7$ and $p = 0.4$ . Compute $P ( 1 \leq X \leq 3 )$ . Round your answer to four decimal places. $P ( 1 \leq X \leq 3 ) =$ __________

Your manufacturing plant produces air bags, and it is known that 50% of them are defective. Fifteen air bags are tested. Find the probability that at least two of them are defective. Round your answer to four decimal places.

You are performing 5 independent Bernoulli trials with $p = 0.2$ and $q = 0.8$ . Calculate the probability of 2 successes. Round your answer to five decimal places if necessary.

You are performing five independent Bernoulli trials with $p = 0.1$ and $q = 0.9$ . Calculate the probability of no failures. Round your answer to four decimal places.

X is a binomial variable with $n = 6$ and $p = 0.6$ . Compute $P ( X \leq 2 )$ . Round your answer to five decimal places.

Quiz 9: Random Variables and Statistics

You are performing seven independent Bernoulli trials with p=0.8p = 0.8p=0.8 and q=0.2q = 0.2q=0.2 . Calculate the probability of three successes. Please, round the answer to four decimal places.

You are performing 5 independent Bernoulli trials with p=0.6p = 0.6p=0.6 and q=0.4q = 0.4q=0.4 . Calculate the probability that it will be at most 2 successes. Round your answer to five decimal places if necessary.

​Assume that on a standardized test of 100 questions, a person has a probability of 86% of answering any particular question correctly. Find the probability of answering between 75 and 85 questions, inclusive, correctly. (Assume independence, and round your answer to four decimal places.) ​

You are performing seven independent Bernoulli trials with p=0.1p = 0.1p=0.1 and q=0.9q = 0.9q=0.9 . Calculate the probability of no successes. Round your answer to four decimal places.

X is a binomial variable with and p=15p = \frac { 1 } { 5 }p=51​ . Compute the probability P(0<X<2) P ( 0 < X < 2 ) P(0<X<2) . Round your answer to four decimal places .

X is a binomial variable with n=4n = 4n=4 and p=12p = \frac { 1 } { 2 }p=21​ . Compute the probability correct to four decimal places P(0≤X≤2)P ( 0 \leq X \leq 2 )P(0≤X≤2) . ​ P(0≤X≤2)≈P ( 0 \leq X \leq 2 ) \approxP(0≤X≤2)≈ __________

In a large on-the-job training program, half of the participants are female and half are male. In a random sample of 6 participants, what is the probability that an investigator will draw at least 2 females Round your answer to four decimal places.

X is a binomial variable with n=6n = 6n=6 and p=0.4p = 0.4p=0.4 . Compute P(X=4) P ( X = 4 ) P(X=4) . Round your answer to five decimal places.

The probability that a randomly chosen citizen-entity of Cygnus is of pension age is approximately 0.6. What is the probability that, in a randomly selected sample of 3 citizen-entities, all of them are of pension age Round your answer to four decimal places. ?

According to a study, the probability that a randomly selected teenager watched a rented video at least once during a week was 0.78. What is the probability that at least 8 teenagers in a group of 10 watched a rented movie at least once last week Express your answer to the nearest hundredth. ?

In a large on-the-job training program, half of the participants are female and half are male. In a random sample of 4 participants, what is the probability that an investigator will draw at least 1 male Please, round your answer to four decimal places.

X is a binomial variable with n=6n = 6n=6 and p=0.4p = 0.4p=0.4 . Compute P(X=5)P ( X = 5 )P(X=5) . Round your answer to four decimal places. ​ P(X=5)=P ( X = 5 ) =P(X=5)= __________

The probability that a randomly selected pound of beef is purchased by McDonald's is 0.09. Ten pounds of beef are chosen at random. What is the probability that exactly two of them are purchased by McDonald's Round your answer to four decimal places.

X is a binomial variable with n=7n = 7n=7 and p=0.4p = 0.4p=0.4 . Compute P(1≤X≤3)P ( 1 \leq X \leq 3 )P(1≤X≤3) . Round your answer to four decimal places. ​ P(1≤X≤3)=P ( 1 \leq X \leq 3 ) =P(1≤X≤3)= __________

Your manufacturing plant produces air bags, and it is known that 50% of them are defective. Fifteen air bags are tested. Find the probability that at least two of them are defective. Round your answer to four decimal places.

You are performing 5 independent Bernoulli trials with p=0.2p = 0.2p=0.2 and q=0.8q = 0.8q=0.8 . Calculate the probability of 2 successes. Round your answer to five decimal places if necessary.

You are performing five independent Bernoulli trials with p=0.1p = 0.1p=0.1 and q=0.9q = 0.9q=0.9 . Calculate the probability of no failures. Round your answer to four decimal places.

X is a binomial variable with n=6n = 6n=6 and p=0.6p = 0.6p=0.6 . Compute P(X≤2) P ( X \leq 2 ) P(X≤2) . Round your answer to five decimal places.

You are performing seven independent Bernoulli trials with $p = 0.8$ and $q = 0.2$ . Calculate the probability of three successes. Please, round the answer to four decimal places.

You are performing 5 independent Bernoulli trials with $p = 0.6$ and $q = 0.4$ . Calculate the probability that it will be at most 2 successes. Round your answer to five decimal places if necessary.

Assume that on a standardized test of 100 questions, a person has a probability of 86% of answering any particular question correctly. Find the probability of answering between 75 and 85 questions, inclusive, correctly. (Assume independence, and round your answer to four decimal places.)

You are performing seven independent Bernoulli trials with $p = 0.1$ and $q = 0.9$ . Calculate the probability of no successes. Round your answer to four decimal places.

X is a binomial variable with and $p = \frac { 1 } { 5 }$ . Compute the probability $P ( 0 < X < 2 )$ . Round your answer to four decimal places .

X is a binomial variable with $n = 4$ and $p = \frac { 1 } { 2 }$ . Compute the probability correct to four decimal places $P ( 0 \leq X \leq 2 )$ . $P ( 0 \leq X \leq 2 ) \approx$ __________

X is a binomial variable with $n = 6$ and $p = 0.4$ . Compute $P ( X = 4 )$ . Round your answer to five decimal places.

X is a binomial variable with $n = 6$ and $p = 0.4$ . Compute $P ( X = 5 )$ . Round your answer to four decimal places. $P ( X = 5 ) =$ __________

X is a binomial variable with $n = 7$ and $p = 0.4$ . Compute $P ( 1 \leq X \leq 3 )$ . Round your answer to four decimal places. $P ( 1 \leq X \leq 3 ) =$ __________

You are performing 5 independent Bernoulli trials with $p = 0.2$ and $q = 0.8$ . Calculate the probability of 2 successes. Round your answer to five decimal places if necessary.

You are performing five independent Bernoulli trials with $p = 0.1$ and $q = 0.9$ . Calculate the probability of no failures. Round your answer to four decimal places.

X is a binomial variable with $n = 6$ and $p = 0.6$ . Compute $P ( X \leq 2 )$ . Round your answer to five decimal places.