Question 1

Find the indicated probability.
-A company manufactures calculators in batches of 55 and claims that the rate of defects is 5%. Find the probability of getting exactly 3 defects in a batch of 55 if the rate of defects is 5%. If a store receives a batch of 55
Calculators and finds that there are 3 defective calculators, do they have any reason to doubt the company's
Claimed rate of defects?

Accepted Answer

The answer of Find the indicated probability.
-A company manufactures calculators...

Question 2

Solve the problem.
-On a multiple choice test with 17 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the number of correct answers.

Accepted Answer

The mean number of correct answers can be found by multiplying the probability of getting a question right (1/4) by the total number of questions (17). Thus, the mean is 17 * (1/4) = 4.25, which rounds to 4.3.

Question 3

Provide an appropriate response.
-If we sample from a small finite population without replacement, the binomial distribution should not be used because the events are not independent. If sampling is done without replacement and the outcomes belong to
One of two types, we can use hypergeometric distribution. If a population has A objects of one type, while the
Remaining B objects are of the other type, and if n objects are sampled without replacement, then the probability
Of getting x objects of type A and (n - x) objects of type B is $P ( x ) = \frac { A ! } { ( A - x ) ! x ! } \cdot \frac { B ! } { ( B - n + x ) ! ( n - x ) ! } \div \frac { ( A + B ) ! } { ( A + B - n ) ! n ! }$ In a relatively easy lottery, a bettor selects 5 numbers from 1 to 13 (without repetition), and a winning 5-number
Combination is later randomly selected. What is the probability of getting all 5 winning numbers? Round your
Answer to four decimal places.

Accepted Answer

The probability of selecting all 5 winning numbers from a set of 13 is calculated using the hypergeometric distribution formula. The probability is given by $\frac{{\binom{5}{5} \cdot \binom{8}{0}}}{{\binom{13}{5}}}$, which simplifies to $\frac{1}{1287} \approx 0.0008$.

Question 4

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth.
-$$\mathrm { n } = 676 ; \mathrm { p } = 0.7$$

Accepted Answer

The answer of Find the mean, µ, for the binomial...

Question 5

Find the indicated probability.
-A slot machine at a hotel is configured so that there is a 1/1200 probability of winning the jackpot on any individual trial. If a guest plays the slot machine 6 times, find the probability of exactly 2 jackpots. If a guest
Told the hotel manager that she had hit two jackpots in 6 plays of the slot machine, would the manager be
Surprised?

Accepted Answer

The answer of Find the indicated probability.
-A slot machine at...

Question 6

Find the standard deviation, $\sigma$ , for the binomial distribution which has the stated values of n and p. Round your answer
to the nearest hundredth.
-$$\mathrm { n } = 48 ; \mathrm { p } = 3 / 5$$

Accepted Answer

The standard deviation of a binomial distribution is given by the formula $\sigma = \sqrt{np(1-p)}$. Substituting the given values, we get $\sigma = \sqrt{(48)(3/5)(2/5)} \approx 3.39$. Therefore, the best choice is B.

Question 7

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth.
-$$\mathrm { n } = 1665 ; \mathrm { p } = 0.57$$

Accepted Answer

The answer of Find the mean, µ, for the binomial...

Question 8

Find the standard deviation, $\sigma$ , for the binomial distribution which has the stated values of n and p. Round your answer
to the nearest hundredth.
-$$\mathrm { n } = 38 ; \mathrm { p } = 0.4$$

Accepted Answer

The answer of Find the standard deviation, $\sigma$ , for...

Question 9

Find the standard deviation, $\sigma$ , for the binomial distribution which has the stated values of n and p. Round your answer
to the nearest hundredth.
-$$\mathrm { n } = 2219 ; \mathrm { p } = 0.63$$

Accepted Answer

The answer of Find the standard deviation, $\sigma$ , for...

Question 10

Solve the problem.
-According to a college survey, 22% of all students work full time. Find the mean for the number of students who work full time in samples of size 16.

Accepted Answer

The mean for the number of students who work full time in samples of size 16 is 22% of 16, which is 3.52.

Question 11

Solve the problem.
-A die is rolled 9 times and the number of times that two shows on the upper face is counted. If this experiment is repeated many times, find the mean for the number of twos.

Accepted Answer

The mean number of twos is calculated using the formula for the expected value of a binomial distribution: n * p, where n is the number of trials (9 rolls) and p is the probability of rolling a two (1/6). Thus, the mean is 9 * (1/6) = 1.5.

Question 12

Find the standard deviation, $\sigma$ , for the binomial distribution which has the stated values of n and p. Round your answer
to the nearest hundredth.
-$$\mathrm { n } = 503 ; \mathrm { p } = 0.7$$

Accepted Answer

The formula for the standard deviation of a binomial distribution is $\sigma = \sqrt{np(1-p)}$. Thus, plugging in $n = 503$ and $p = 0.7$, we get $\sigma=\sqrt{503\cdot0.7\cdot0.3}\approx 10.28$. Round to the nearest hundredth gives us $\boxed{	extbf{(B)}\ 10.28}$.

Question 13

Provide an appropriate response.
-If a procedure meets all the conditions of a binomial distribution except that the number of trials is not fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given
By $$P ( x ) = p ( 1 - p ) ^ { x - 1 }$$ , where p is the probability of success on any one trial. Assume that the probability of
Choosing a yellow piece of candy in a bag of hard candy is 0.234. Find the probability that the first yellow candy
Is found in the eighth inspected. Round your answer to the nearest thousandth.

Accepted Answer

The answer of Provide an appropriate response.
-If a procedure meets...

Question 14

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth.
-$$\mathrm { n } = 2571 ; \mathrm { p } = 0.63$$

Accepted Answer

The mean of a binomial distribution is given by $\mu = np$, so $\mu = 2571\cdot0.63 \approx 1619.7$. Rounding to the nearest tenth, we get $\boxed{	extbf{(A) }\mu=1619.7}$.

Question 15

Find the standard deviation, $\sigma$ , for the binomial distribution which has the stated values of n and p. Round your answer
to the nearest hundredth.
-$$\mathrm { n } = 29 ; \mathrm { p } = 0.2$$

Accepted Answer

The standard deviation for a binomial distribution is calculated using the formula $\sigma = \sqrt{n \cdot p \cdot (1-p)}$. Substituting the given values, $\sigma = \sqrt{29 \cdot 0.2 \cdot 0.8} = \sqrt{4.64} \approx 2.15$.

Question 16

Find the indicated probability.
-Suppose that 14% of people are left handed. If 9 people are selected at random, what is the probability that exactly 2 of them are left handed?

Accepted Answer

The answer of Find the indicated probability.
-Suppose that 14% of...

Question 17

Provide an appropriate response.
-The binomial distribution applies only to cases involving two types of outcomes, whereas the multinomial distribution involves more than two categories. Suppose we have three types of mutually exclusive outcomes
Denoted by A, B, and C $\text { Let } \mathrm { P } ( \mathrm { A } ) = \mathrm { p } _ { 1 } , \mathrm { P } ( \mathrm { B } ) = \mathrm { p } _ { 2 } , \mathrm { P } ( \mathrm { C } ) = \mathrm { p } _ { 3 }$ . In n independent trials, the probability of $\mathrm { X } _ { 1 }$ outcomes of type A, $X 2$ outcomes of type B, and $X3$ outcomes of type C is given by $\frac { \mathrm { n } ! } { \left( \mathrm { x } _ { 1 } \right) ! \left( \mathrm { x } _ { 2 } \right) ! \left( \mathrm { x } _ { 3 } \right) ! } \cdot \mathrm { p } ^ { \mathrm { x } } 1 \cdot \mathrm { p } ^ { \mathrm { x } _ { 2 } } \cdot \mathrm { p } _ { 3 } ^ { \mathrm { x } _ { 3 } }$ A genetics experiment involves four mutually exclusive genotypes identified as A, B, C, and D, and they are all
Equally likely. If 10 offspring are tested, find the probability of getting exactly 2 A's,3 B's,3 C's, and 2 D's by
Expanding the above expression so that it applies to four types of outcomes instead of only three. Round your
Answer to five decimal places.

Accepted Answer

The answer of Provide an appropriate response.
-The binomial distribution applies...

Question 18

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth.
-$$\mathrm { n } = 38 ; \mathrm { p } = 3 / 5$$

Accepted Answer

The answer of Find the mean, µ, for the binomial...

Question 19

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth.
-$$\mathrm { n } = 38 ; \mathrm { p } = 0.2$$

Accepted Answer

The answer of Find the mean, µ, for the binomial...

Question 20

Find the standard deviation, $\sigma$ , for the binomial distribution which has the stated values of n and p. Round your answer
to the nearest hundredth.
-$$\mathrm { n } = 1680 ; \mathrm { p } = 0.57$$

Accepted Answer

The answer of Find the standard deviation, $\sigma$ , for...

Quiz 5: Discrete Probability Distributions

Solve the problem. -On a multiple choice test with 17 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the number of correct answers.

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - $\mathrm { n } = 676 ; \mathrm { p } = 0.7$

Find the standard deviation, $\sigma$ , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - $\mathrm { n } = 48 ; \mathrm { p } = 3 / 5$

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - $\mathrm { n } = 1665 ; \mathrm { p } = 0.57$

Find the standard deviation, $\sigma$ , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - $\mathrm { n } = 38 ; \mathrm { p } = 0.4$

Find the standard deviation, $\sigma$ , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - $\mathrm { n } = 2219 ; \mathrm { p } = 0.63$

Solve the problem. -According to a college survey, 22% of all students work full time. Find the mean for the number of students who work full time in samples of size 16.

Solve the problem. -A die is rolled 9 times and the number of times that two shows on the upper face is counted. If this experiment is repeated many times, find the mean for the number of twos.

Find the standard deviation, $\sigma$ , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - $\mathrm { n } = 503 ; \mathrm { p } = 0.7$

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - $\mathrm { n } = 2571 ; \mathrm { p } = 0.63$

Find the standard deviation, $\sigma$ , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - $\mathrm { n } = 29 ; \mathrm { p } = 0.2$

Find the indicated probability. -Suppose that 14% of people are left handed. If 9 people are selected at random, what is the probability that exactly 2 of them are left handed?

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - $\mathrm { n } = 38 ; \mathrm { p } = 3 / 5$

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - $\mathrm { n } = 38 ; \mathrm { p } = 0.2$

Find the standard deviation, $\sigma$ , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - $\mathrm { n } = 1680 ; \mathrm { p } = 0.57$

Quiz 5: Discrete Probability Distributions

Solve the problem. -On a multiple choice test with 17 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the number of correct answers.

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - n=676;p=0.7\mathrm { n } = 676 ; \mathrm { p } = 0.7n=676;p=0.7

Find the standard deviation, σ\sigmaσ , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - n=48;p=3/5\mathrm { n } = 48 ; \mathrm { p } = 3 / 5n=48;p=3/5

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - n=1665;p=0.57\mathrm { n } = 1665 ; \mathrm { p } = 0.57n=1665;p=0.57

Find the standard deviation, σ\sigmaσ , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - n=38;p=0.4\mathrm { n } = 38 ; \mathrm { p } = 0.4n=38;p=0.4

Find the standard deviation, σ\sigmaσ , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - n=2219;p=0.63\mathrm { n } = 2219 ; \mathrm { p } = 0.63n=2219;p=0.63

Solve the problem. -According to a college survey, 22% of all students work full time. Find the mean for the number of students who work full time in samples of size 16.

Solve the problem. -A die is rolled 9 times and the number of times that two shows on the upper face is counted. If this experiment is repeated many times, find the mean for the number of twos.

Find the standard deviation, σ\sigmaσ , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - n=503;p=0.7\mathrm { n } = 503 ; \mathrm { p } = 0.7n=503;p=0.7

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - n=2571;p=0.63\mathrm { n } = 2571 ; \mathrm { p } = 0.63n=2571;p=0.63

Find the standard deviation, σ\sigmaσ , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - n=29;p=0.2\mathrm { n } = 29 ; \mathrm { p } = 0.2n=29;p=0.2

Find the indicated probability. -Suppose that 14% of people are left handed. If 9 people are selected at random, what is the probability that exactly 2 of them are left handed?

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - n=38;p=3/5\mathrm { n } = 38 ; \mathrm { p } = 3 / 5n=38;p=3/5

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - n=38;p=0.2\mathrm { n } = 38 ; \mathrm { p } = 0.2n=38;p=0.2

Find the standard deviation, σ\sigmaσ , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - n=1680;p=0.57\mathrm { n } = 1680 ; \mathrm { p } = 0.57n=1680;p=0.57

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - $\mathrm { n } = 676 ; \mathrm { p } = 0.7$

Find the standard deviation, $\sigma$ , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - $\mathrm { n } = 48 ; \mathrm { p } = 3 / 5$

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - $\mathrm { n } = 1665 ; \mathrm { p } = 0.57$

Find the standard deviation, $\sigma$ , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - $\mathrm { n } = 38 ; \mathrm { p } = 0.4$

Find the standard deviation, $\sigma$ , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - $\mathrm { n } = 2219 ; \mathrm { p } = 0.63$

Find the standard deviation, $\sigma$ , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - $\mathrm { n } = 503 ; \mathrm { p } = 0.7$

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - $\mathrm { n } = 2571 ; \mathrm { p } = 0.63$

Find the standard deviation, $\sigma$ , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - $\mathrm { n } = 29 ; \mathrm { p } = 0.2$

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - $\mathrm { n } = 38 ; \mathrm { p } = 3 / 5$

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - $\mathrm { n } = 38 ; \mathrm { p } = 0.2$

Find the standard deviation, $\sigma$ , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - $\mathrm { n } = 1680 ; \mathrm { p } = 0.57$