Question 1

Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using
the table. $$\begin{array}{l}
\text {\quad\quad\quad\quad\quad\quad\quad\quad Probabilities of Girls }\
\begin{array} { c | c | c | c | c | c } 
x ( \text { girls) } & P ( x ) & x \text { (girls) } & P ( x ) & x \text { (girls) } & P ( x ) \
\hline 0 & 0.000 & 5 & 0.122 & 10 & 0.061 \
1 & 0.001 & 6 & 0.183 & 11 & 0.022 \
2 & 0.006 & 7 & 0.209 & 12 & 0.006 \
3 & 0.022 & 8 & 0.183 & 13 & 0.001 \
4 & 0.061 & 9 & 0.122 & 14 & 0.000
\end{array}
\end{array}$$
-Find the probability of selecting 12 or more girls.

Accepted Answer

The probability of selecting 12 or more girls is the sum of the probabilities for x = 12, 13, and 14, which is 0.006 + 0.001 + 0.000 = 0.007.

Question 2

Suppose that a law enforcement group studying traffic violations determines that the accompanying table describes the probability distribution for five randomly selected people, where X is the number that have received a speeding ticket in the last 2 years. Is it unusual to find no speeders among five randomly selected people? $$\begin{array} { c | c } 
\mathrm { x } & \mathrm { P } ( \mathrm { x } ) \
\hline 0 & 0.08 \
1 & 0.18 \
2 & 0.25 \
3 & 0.22 \
4 & 0.19 \
5 & 0.08
\end{array}$$

Accepted Answer

The probability of finding no speeders among five randomly selected people is 0.08, which is not extremely low, so it is not considered unusual.

Question 3

Find the indicated probability. Round to three decimal places.
-In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, that is the probability that no more than 6 belong to an ethnic minority?

Accepted Answer

The probability can be calculated using the binomial distribution formula. With p = 0.33, n = 10, and x ≤ 6, the cumulative probability is approximately 0.982.

Question 4

Find the standard deviation, σ, for the binomial distribution which has the stated values of n and p. Round your answer
to the nearest hundredth.
-$\mathrm { n } = 1617 ; \mathrm { p } = 0.57$

Accepted Answer

The standard deviation for a binomial distribution is given by the formula:$\sigma = \sqrt{np(1-p)}$Plugging in the given values, we get:$\sigma = \sqrt{1617 * 0.57 * (1-0.57)} = 19.91$Therefore, the correct answer is A.

Question 5

A tennis player makes a successful first serve 46% of the time. If she serves 8 times, what is the probability that she gets exactly 3 first serves in? Assume that each serve is independent of the others.

Accepted Answer

The answer of A tennis player makes a successful first...

Question 6

Use the given values of n and p to find the minimum usual value $\mu - 2 \sigma \text { and the maximum usual value } \mu + 2 \sigma \text {. }$ . Round
your answer to the nearest hundredth unless otherwise noted.
-$\mathrm { n } = 166 , \mathrm { p } = 0.15$

Accepted Answer

The answer of Use the given values of n and...

Question 7

In a certain town, 30% of voters favor a given ballot measure. For groups of 34 voters, find the variance for the number who favor the measure.

Accepted Answer

The answer of In a certain town, 30% of voters...

Question 8

A company manufactures batteries in batches of 25 and there is a 3% rate of defects. Find the mean number of defects per batch.

Accepted Answer

The mean number of defects per batch is calculated by multiplying the batch size by the defect rate: 25 * 0.03 = 0.75, which rounds to 0.8.

Question 9

Find the mean, $\mu$ , for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth.
-$\mathrm { n } = 37 ; \mathrm { p } = 0.2$

Accepted Answer

The answer of Find the mean, $\mu$ , for the...

Question 10

Find the indicated probability. Round to three decimal places.
-Find the probability of at least 2 girls in 8 births. Assume that male and female births are equally likely and that the births are independent events.

Accepted Answer

The probability of at least 2 girls in 8 births can be found by calculating 1 minus the probability of having 0 or 1 girl. Using the binomial probability formula, the probability of 0 girls is (0.5)^8 and the probability of 1 girl is 8*(0.5)^8. Adding these probabilities and subtracting from 1 gives approximately 0.965.

Question 11

Find the indicated probability. Round to three decimal places.
-A test consists of 10 true/false questions. To pass the test a student must answer at least 9 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?

Accepted Answer

The probability of guessing each question correctly is 0.5. Using the binomial probability formula, calculate the probability of getting exactly 9 or 10 correct answers out of 10. The sum of these probabilities is approximately 0.011.

Question 12

Identify the given random variable as being discrete or continuous.
-The number of freshmen in the required course, English 101

Accepted Answer

The variable "number of freshmen in the required course, English 101" can only take on whole number values, making it a discrete random variable. Therefore, the best choice is B.

Question 13

A company manufactures batteries in batches of 22 and there is a 3% rate of defects. Find the variance for the number of defects per batch.

Accepted Answer

The answer of A company manufactures batteries in batches of...

Question 14

Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than $\mu - 2 \sigma \text { or greater than } \mu + 2 \sigma \text {. }$
-The Acme Candy Company claims that 60% of the jawbreakers it produces weigh more than .4 ounces. Suppose that 800 jawbreakers are selected at random from the production lines. Would it be unusual for this sample of 800 to contain 552 jawbreakers that weigh more than .4 ounces?

Accepted Answer

The mean number of jawbreakers that weigh more than .4 ounces is 0.6 * 800 = 480. The standard deviation is sqrt(0.6 * 0.4 * 800) = 16.97. So, the unusual values are less than 480 - 2 * 16.97 = 446.16 or greater than 480 + 2 * 16.97 = 513.84. Since 552 is greater than 513.84, it would be unusual for this sample of 800 to contain 552 jawbreakers that weigh more than .4 ounces.

Question 15

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places.
-$\mathrm { n } = 6 , \mathrm { x } = 3 , \mathrm { p } = \frac { 1 } { 6 }$

Accepted Answer

The answer of Assume that a procedure yields a binomial...

Question 16

The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 20. Find the standard deviation for the number of seeds germinating in each batch.

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 (20 seeds), and p is the probability of success (0.7). Thus, √(20 * 0.7 * 0.3) = √4.2 ≈ 2.05, which rounds to 2.

Question 17

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 A slot machine at a hotel is...

Question 18

Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using
the table. $$\begin{array}{l}
\text {\quad\quad\quad\quad\quad\quad\quad\quad Probabilities of Girls }\
\begin{array} { c | c | c | c | c | c } 
x ( \text { girls) } & \mathrm { P } ( \mathrm { x } ) & \mathrm { x } ( \text { girls) } & \mathrm { P } ( \mathrm { x } ) & \mathrm { x } ( \text { girls) } & \mathrm { P } ( \mathrm { x } ) \
\hline 0 & 0.000 & 5 & 0.122 & 10 & 0.061 \
1 & 0.001 & 6 & 0.183 & 11 & 0.022 \
2 & 0.006 & 7 & 0.209 & 12 & 0.006 \
3 & 0.022 & 8 & 0.183 & 13 & 0.001 \
4 & 0.061 & 9 & 0.122 & 14 & 0.000
\end{array}
\end{array}$$
-Find the probability of selecting exactly 8 girls.

Accepted Answer

The probability of selecting exactly 8 girls is given as 0.183 in the table.

Question 19

Find the mean of the given probability distribution.
-The random variable x is the number of houses sold by a realtor in a single month at the Sendsom's Real Estate office. Its probability distribution is as follows.

$\begin{array}{c|c}
\text { Houses Sold }(\mathrm{x}) & \text { Probability } \mathrm{P}(\mathrm{x}) \
\hline 0 & 0.24 \
1 & 0.01 \
2 & 0.12 \
3 & 0.16 \
4 & 0.01 \
5 & 0.14 \
6 & 0.11 \
7 & 0.21
\end{array}$

Accepted Answer

The answer of Find the mean of the given probability...

Question 20

A die is rolled 19 times and the number of twos that come up is tallied. If this experiment is repeated many times, find the standard deviation for the number of twos.

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 (19), and p is the probability of success (rolling a two, which is 1/6). Plugging in these values gives √(19 * 1/6 * 5/6) ≈ 1.6.

Quiz 5: Discrete Probability Distributions

Find the indicated probability. Round to three decimal places. -In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, that is the probability that no more than 6 belong to an ethnic minority?

Find the standard deviation, σ, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - $\mathrm { n } = 1617 ; \mathrm { p } = 0.57$

A tennis player makes a successful first serve 46% of the time. If she serves 8 times, what is the probability that she gets exactly 3 first serves in? Assume that each serve is independent of the others.

Use the given values of n and p to find the minimum usual value $\mu - 2 \sigma \text { and the maximum usual value } \mu + 2 \sigma \text {. }$ . Round your answer to the nearest hundredth unless otherwise noted. - $\mathrm { n } = 166 , \mathrm { p } = 0.15$

In a certain town, 30% of voters favor a given ballot measure. For groups of 34 voters, find the variance for the number who favor the measure.

A company manufactures batteries in batches of 25 and there is a 3% rate of defects. Find the mean number of defects per batch.

Find the mean, $\mu$ , for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - $\mathrm { n } = 37 ; \mathrm { p } = 0.2$

Find the indicated probability. Round to three decimal places. -Find the probability of at least 2 girls in 8 births. Assume that male and female births are equally likely and that the births are independent events.

Find the indicated probability. Round to three decimal places. -A test consists of 10 true/false questions. To pass the test a student must answer at least 9 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?

Identify the given random variable as being discrete or continuous. -The number of freshmen in the required course, English 101

A company manufactures batteries in batches of 22 and there is a 3% rate of defects. Find the variance for the number of defects per batch.

The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 20. Find the standard deviation for the number of seeds germinating in each batch.

A die is rolled 19 times and the number of twos that come up is tallied. If this experiment is repeated many times, find the standard deviation for the number of twos.

Quiz 5: Discrete Probability Distributions

Find the indicated probability. Round to three decimal places. -In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, that is the probability that no more than 6 belong to an ethnic minority?

Find the standard deviation, σ, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - n=1617;p=0.57\mathrm { n } = 1617 ; \mathrm { p } = 0.57n=1617;p=0.57

A tennis player makes a successful first serve 46% of the time. If she serves 8 times, what is the probability that she gets exactly 3 first serves in? Assume that each serve is independent of the others.

In a certain town, 30% of voters favor a given ballot measure. For groups of 34 voters, find the variance for the number who favor the measure.

A company manufactures batteries in batches of 25 and there is a 3% rate of defects. Find the mean number of defects per batch.

Find the mean, μ\muμ , for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - n=37;p=0.2\mathrm { n } = 37 ; \mathrm { p } = 0.2n=37;p=0.2

Find the indicated probability. Round to three decimal places. -Find the probability of at least 2 girls in 8 births. Assume that male and female births are equally likely and that the births are independent events.

Find the indicated probability. Round to three decimal places. -A test consists of 10 true/false questions. To pass the test a student must answer at least 9 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?

Identify the given random variable as being discrete or continuous. -The number of freshmen in the required course, English 101

A company manufactures batteries in batches of 22 and there is a 3% rate of defects. Find the variance for the number of defects per batch.

The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 20. Find the standard deviation for the number of seeds germinating in each batch.

A die is rolled 19 times and the number of twos that come up is tallied. If this experiment is repeated many times, find the standard deviation for the number of twos.

Find the standard deviation, σ, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - $\mathrm { n } = 1617 ; \mathrm { p } = 0.57$

Find the mean, $\mu$ , for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - $\mathrm { n } = 37 ; \mathrm { p } = 0.2$