Question 1

Find the standard deviation of the binomial distribution for which n = 1000 and p = 0.94.
A)7.51
B)56.4
C)940
D)6.31

Accepted Answer

The standard deviation ($\sigma$) of a binomial distribution is given by the formula $\sigma = \sqrt{n \cdot p \cdot (1-p)}$, where $n$ is the number of trials and $p$ is the probability of success on each trial. Substituting $n = 1000$ and $p = 0.94$ into the formula gives $\sigma = \sqrt{1000 \cdot 0.94 \cdot (1-0.94)} = \sqrt{1000 \cdot 0.94 \cdot 0.06} = \sqrt{56.4} \approx 7.51$.

Question 2

Decide whether the experiment is a binomial experiment. If it is not, explain why. Testing a pain reliever using
740 people to determine if it is effective. The random variable represents the number of people who find the
pain reliever to be effective.

Accepted Answer

The answer of Decide whether the experiment is a binomial...

Question 3

Decide whether the experiment is a binomial experiment. If it is not, explain why. You roll a die 100 times. The
random variable represents the number that appears on each roll of the die.

Accepted Answer

The answer of Decide whether the experiment is a binomial...

Question 4

Decide whether the experiment is a binomial experiment. If it is not, explain why. Surveying 600 prisoners to
see whether they are serving time for their first offense. The random variable represents the number of
prisoners serving time for their first offense.

Accepted Answer

The answer of Decide whether the experiment is a binomial...

Question 5

Decide whether the experiment is a binomial experiment. If it is not, explain why. You test four pain relievers.
The random variable represents the pain reliever that is most effective.

Accepted Answer

The answer of Decide whether the experiment is a binomial...

Question 6

Find the mean of the binomial distribution for which n = 40 and p = 0.2.
A)8
B)2.53
C)20
D)40

Accepted Answer

The mean ($\mu$) of a binomial distribution is calculated using the formula $\mu = np$, where $n$ is the number of trials and $p$ is the probability of success on a single trial. For $n = 40$ and $p = 0.2$, the mean is $40 \times 0.2 = 8$.

Question 7

Decide whether the experiment is a binomial experiment. If it is not, explain why. Surveying 250 prisoners to
see how many crimes in which they were convicted. The random variable represents the number of crimes in
which each prisoner was convicted.

Accepted Answer

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Question 8

Decide whether the experiment is a binomial experiment. If it is not, explain why. You observe the gender of
the next 250 babies born at a local hospital. The random variable represents the number of girls.

Accepted Answer

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Question 9

From the probability distribution, find the mean and standard deviation for the random variable x, which
represents the number of cars per household in a town of 1000 households. $$\begin{array} { c | c } 
\mathrm { x } & \mathrm { P } ( \mathrm { x } ) \
\hline 0 & 0.125 \
1 & 0.428 \
2 & 0.256 \
3 & 0.108 \
4 & 0.083
\end{array}$$

Accepted Answer

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Question 10

Decide whether the experiment is a binomial experiment. If it is not, explain why. Each week, a man plays a
game in which he has a 39% chance of winning. The random variable is the number of times he wins in 51
weeks.

Accepted Answer

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Question 11

Decide whether the experiment is a binomial experiment. If it is not, explain why. You spin a number wheel
that has 19 numbers 450 times. The random variable represents the winning numbers on each spin of the
wheel.

Accepted Answer

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Question 12

In a recent survey, 80% of the community favored building a police substation in their neighborhood. If 15 citizens are chosen, what is the mean number favoring the substation?
A)12
B)15
C)8
D)10

Accepted Answer

The mean number favoring the substation can be calculated by multiplying the total number of citizens chosen by the percentage favoring the substation: 15 citizens * 80% = 12 citizens.

Question 13

In a recent survey, 80% of the community favored building a police substation in their neighborhood. If 15 citizens are chosen, what is the standard deviation of the number favoring the substation?
A)1.55
B)2.40
C)0.98
D)0.55

Accepted Answer

The standard deviation for a binomial distribution is calculated using the formula √(n * p * (1-p)), where n is the number of trials (15), and p is the probability of success (0.8). Plugging in the values gives √(15 * 0.8 * 0.2) = 1.55.

Question 14

In one city, 24% of adults smoke. In groups of size 130 of adults, what is the variance of the number that smoke ?
A)23.71
B)4.87
C)31.2
D)11.86

Accepted Answer

The variance of the number that smoke in groups of size 130 can be calculated using the formula for the variance of a binomial distribution, which is $np(1-p)$, where $n$ is the size of the group (130 in this case) and $p$ is the probability of an adult smoking (24% or 0.24). Thus, the variance is $130 \times 0.24 \times (1-0.24) = 130 \times 0.24 \times 0.76 = 23.712$, which rounds to 23.71.

Question 15

In a raffle, 1,000 tickets are sold for $2 each. One ticket will be randomly selected and the winner will receive a laptop computer valued at $1200. What is the expected value for a person that buys one ticket?
A)-$0.80
B)$0.8
C)$1.20
D)-$1.20

Accepted Answer

The expected value (EV) is calculated by multiplying the probability of winning and the value of the prize, then adding the product of the probability of losing and the loss (ticket cost). Probability of winning = 1/1000, value of prize = $1200, probability of losing = 999/1000, cost of ticket = $2. EV = (1/1000)*$1200 + (999/1000)*(-$2) = $1.20 - $1.998 = -$0.80.

Question 16

A test consists of 700 true or false questions. If the student guesses on each question, what is the mean number of correct answers?
A)350
B)0
C)700
D)140

Accepted Answer

For each question, the probability of guessing correctly is 1/2. Therefore, the mean number of correct answers out of 700 questions is 700 * (1/2) = 350.

Question 17

Find the variance of the binomial distribution for which n = 800 and p = 0.87.
A)90.48
B)9.51
C)696
D)32.54

Accepted Answer

The variance ($\sigma^2$) of a binomial distribution is given by the formula $\sigma^2 = np(1-p)$, where $n$ is the number of trials and $p$ is the probability of success on a single trial. Substituting $n = 800$ and $p = 0.87$, we get $\sigma^2 = 800 \times 0.87 \times (1 - 0.87) = 800 \times 0.87 \times 0.13 = 90.48$.

Question 18

The probability that a house in an urban area will be burglarized is 5%. If 20 houses are randomly selected, what is the mean of the number of houses burglarized?
A)1
B)10
C)0.5
D)1.5

Accepted Answer

The mean of a binomial distribution is equal to the product of the number of trials and the probability of success. In this case, the number of trials is 20 and the probability of success is 0.05, so the mean is 20 * 0.05 = 1.

Question 19

A test consists of 800 true or false questions. If the student guesses on each question, what is the standard deviation of the number of correct answers?
A)14.14
B)0
C)2
D)20

Accepted Answer

The standard deviation for a binomial distribution is given by the formula $\sqrt{n \cdot p \cdot (1-p)}$, where $n$ is the number of trials (in this case, 800 questions), and $p$ is the probability of success on each trial (for a true/false question, $p = 0.5$). Plugging in these values, we get $\sqrt{800 \cdot 0.5 \cdot 0.5} = \sqrt{200} = 14.14$.

Question 20

Decide whether the experiment is a binomial experiment. If it is not, explain why. Selecting five cards, one at a
time without replacement, from a standard deck of cards. The random variable is the number of red cards
obtained.

Accepted Answer

The answer of Decide whether the experiment is a binomial...

Quiz 4: Discrete Probability Distributions

Find the standard deviation of the binomial distribution for which n = 1000 and p = 0.94.

Decide whether the experiment is a binomial experiment. If it is not, explain why. Testing a pain reliever using 740 people to determine if it is effective. The random variable represents the number of people who find the pain reliever to be effective.

Decide whether the experiment is a binomial experiment. If it is not, explain why. You roll a die 100 times. The random variable represents the number that appears on each roll of the die.

Decide whether the experiment is a binomial experiment. If it is not, explain why. Surveying 600 prisoners to see whether they are serving time for their first offense. The random variable represents the number of prisoners serving time for their first offense.

Decide whether the experiment is a binomial experiment. If it is not, explain why. You test four pain relievers. The random variable represents the pain reliever that is most effective.

Find the mean of the binomial distribution for which n = 40 and p = 0.2.

Decide whether the experiment is a binomial experiment. If it is not, explain why. Surveying 250 prisoners to see how many crimes in which they were convicted. The random variable represents the number of crimes in which each prisoner was convicted.

Decide whether the experiment is a binomial experiment. If it is not, explain why. You observe the gender of the next 250 babies born at a local hospital. The random variable represents the number of girls.

Decide whether the experiment is a binomial experiment. If it is not, explain why. Each week, a man plays a game in which he has a 39% chance of winning. The random variable is the number of times he wins in 51 weeks.

Decide whether the experiment is a binomial experiment. If it is not, explain why. You spin a number wheel that has 19 numbers 450 times. The random variable represents the winning numbers on each spin of the wheel.

In a recent survey, 80% of the community favored building a police substation in their neighborhood. If 15 citizens are chosen, what is the mean number favoring the substation?

In a recent survey, 80% of the community favored building a police substation in their neighborhood. If 15 citizens are chosen, what is the standard deviation of the number favoring the substation?

In one city, 24% of adults smoke. In groups of size 130 of adults, what is the variance of the number that smoke ?

In a raffle, 1,000 tickets are sold for $2 each. One ticket will be randomly selected and the winner will receive a laptop computer valued at $1200. What is the expected value for a person that buys one ticket?

A test consists of 700 true or false questions. If the student guesses on each question, what is the mean number of correct answers?

Find the variance of the binomial distribution for which n = 800 and p = 0.87.

The probability that a house in an urban area will be burglarized is 5%. If 20 houses are randomly selected, what is the mean of the number of houses burglarized?

A test consists of 800 true or false questions. If the student guesses on each question, what is the standard deviation of the number of correct answers?

Decide whether the experiment is a binomial experiment. If it is not, explain why. Selecting five cards, one at a time without replacement, from a standard deck of cards. The random variable is the number of red cards obtained.