Question 1

A certain baseball player hits a home run in 3% of his at-bats. Consider his at-bats as independent events. How many home runs do we expect the baseball player to hit in 600 at-bats?
A) 17.46
B) 18
C) 3
D) 603

Accepted Answer

The answer of A certain baseball player hits a home...

Question 2

The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.30 ounces and a standard deviation of 0.20 ounce. Each can holds a maximum of 12.50 ounces of soda. Every can that has more than 12.50 ounces of soda poured into it
Causes a spill and the can must go through a special cleaning process before it can be sold. What is the probability that a randomly selected can will need to go through this process?
A) .8413
B) .6587
C) .1587
D) .3413

Accepted Answer

The probability is found by calculating the area to the right of 12.50 ounces in the normal distribution. The z-score is (12.50 - 12.30) / 0.20 = 1. The probability of a z-score greater than 1 is 0.1587.

Question 3

It is against the law to discriminate against job applicants because of race, religion, sex, or age. Of the individuals who apply for an accountant's position in a large corporation, 38 are over 45 years old. If the company decides to choose 88 of a very large number of applicants for closer credential screening, claiming that the selection will be random and not age-biased, what is the $z$-value associated with fewer than 42 of those chosen being over 45 years old? (Assume that the applicant pool is large enough so that $x$, the number in the sample over 45 years old, has a binomial probability distribution.)

Accepted Answer

The answer of It is against the law to discriminate...

Question 4

Explain why the following is or is not a valid probability distribution for the discrete random variable x. 
$$\begin{array} { | c | c | c | c | c | c | } 
\hline x & 0 & 2 & 4 & 6 & 8 \
\hline p ( x ) & - .1 & .1 & .2 & .3 & .5 \
\hline
\end{array}$$

Accepted Answer

The answer of Explain why the following is or is...

Question 5

The rate of return for an investment can be described by a normal distribution with  and standard deviation 3%. What is the probability that the rate of return for the investment will be at least 43.5%?

Accepted Answer

The answer of The rate of return for an investment...

Question 6

The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 8.5 to 10.5 millimeters. Any ball bearing with a diameter of
Over 10.25 millimeters or under 8.75 millimeters is considered defective. What is the probability
That a randomly selected ball bearing is defective?
A) .50
B) 0
C) .75
D) .25

Accepted Answer

The defective range is from 8.5 to 8.75 and from 10.25 to 10.5. Each range is 0.25 mm, so the total defective range is 0.5 mm. The total range is 2 mm (10.5 - 8.5). The probability is 0.5/2 = 0.25.

Question 7

Explain why the following is or is not a valid probability distribution for the discrete random variable x. 
$$\begin{array} { | c | c | c | c | c | c | } 
\hline x & 10 & 20 & 30 & 40 & 50 \
\hline p ( x ) & .3 & .2 & .2 & .2 & .2 \
\hline
\end{array}$$

Accepted Answer

The answer of Explain why the following is or is...

Question 8

Classify the following random variable according to whether it is discrete or continuous. The number of phone calls to the attendance office of a high school on any given school day
A) discrete
B) continuous

Accepted Answer

The number of phone calls is a countable quantity, making it a discrete random variable.

Question 9

Classify the following random variable according to whether it is discrete or continuous. The blood pressures of a group of students the day before the final exam
A) discrete
B) continuous

Accepted Answer

Blood pressure is a continuous variable because it can take on any value within a certain range.

Question 10

Classify the following random variable according to whether it is discrete or continuous. The number of goals scored in a soccer game
A) continuous
B) discrete

Accepted Answer

The number of goals scored in a soccer game can only take on integer values, so it is a discrete random variable.

Question 11

Consider the given discrete probability distribution.

$\begin{array}{|c|c|c|c|c|c|}
\hline x & 1 & 2 & 3 & 4 & 5 \
\hline p(x) & .1 & .2 & .2 & .3 & .2 \
\hline
\end{array}$
a. Find $\mu = E ( x )$.
b. Find $\sigma = \sqrt { E \left[ ( x - \mu ) ^ { 2 } \right] }$.
c. Find the probability that the value of $x$ falls within one standard deviation of the mean. Compare this result to the Empirical Rule.

Accepted Answer

The answer of Consider the given discrete probability distribution.

\(\begin{array}{|c|c|c|c|c|c|}
\hline...

Question 12

The continuity correction factor is the name given to the .5 adjustment necessary when estimating the binomial with the normal distribution.

Accepted Answer

The continuity correction factor is used to adjust for the fact that the normal distribution is a continuous distribution, while the binomial distribution is a discrete distribution. This adjustment involves adding or subtracting 0.5 to the endpoints of the interval when using the normal distribution to approximate the binomial distribution.

Question 13

You test 3 items from a lot of 12. What is the probability that you will test no defective items if the lot contains 2 defective items?

Accepted Answer

The answer of You test 3 items from a lot...

Question 14

A small life insurance company has determined that on the average it receives 5 death claims per day. Find the probability that the company receives at least seven death claims on a randomly selected day.

Accepted Answer

The answer of A small life insurance company has determined...

Question 15

$\text { Compute } \left( \begin{array} { l } 
4 \
4
\end{array} \right)$

A) 16
B) 4
C) 1
D) 6

Accepted Answer

The answer of \(\text { Compute } \left( \begin{array} {...

Question 16

Consider the given discrete probability distribution. Find $P ( x < 2 \text { or } x > 3 ) \text {. }$
 $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & 1 & 2 & 3 & 4 & 5 \
\hline p ( x ) & .1 & .2 & .2 & .3 & .2 \
\hline
\end{array}$$

Accepted Answer

The answer of Consider the given discrete probability distribution. Find...

Question 17

The preventable monthly loss at a company has a normal distribution with a mean of $7800 standard deviation of $30. A new policy was put into place, and the preventable loss the next month was $7620. What inference can you make about the new policy?
A) The new policy is probably less effective than the one it replaced.
B) Because the probability that the monthly loss would be as low as $7620 is small, the new policy is working.
C) Because the probability that the monthly loss would be as low as $7620 is not very small, the new policy is not working.
D) While the probability that the monthly loss would be as low as $7620 is small, it is not unexpected.

Accepted Answer

The preventable loss of $7620 is lower than the mean of $7800, and given the standard deviation of $30, this is more than 6 standard deviations below the mean, which is a rare event in a normal distribution, suggesting the new policy is effective.

Question 18

$$\begin{array}{l}
\text { Consider the given discrete probability distribution. Find } P ( x \leq 4 ) \text {. }\
\begin{array} { | c | c | c | c | c | c | c | } 
\hline x & 0 & 1 & 2 & 3 & 4 & 5 \
\hline p ( x ) & .30 & .25 & .20 & .15 & .05 & .05 \
\hline
\end{array}
\end{array}$$
A) .95
B) .05
C) .10
D) .90

Accepted Answer

The answer of \[\begin{array}{l}
\text { Consider the given discrete probability...

Question 19

The exponential distribution has the property that its mean equals its standard deviation.

Accepted Answer

This statement is true. Specifically, if X is an exponentially distributed random variable with parameter λ, then its mean is equal to 1/λ and its standard deviation is also equal to 1/λ. Therefore, the mean and standard deviation are equal for any value of λ.

Question 20

Suppose the candidate pool for two appointed positions includes 6 women and 9 men. All candidates were told that the positions were randomly filled. Find the probability that two men are selected to fill the appointed positions.
A) .343
B) .160
C) .143
D) .360

Accepted Answer

The probability of selecting two men is 9/15 * 8/14 = 36/210 = 0.1714 or 17.14%

Quiz 4: Random Variables and Probability Distributions

A certain baseball player hits a home run in 3% of his at-bats. Consider his at-bats as independent events. How many home runs do we expect the baseball player to hit in 600 at-bats?

Explain why the following is or is not a valid probability distribution for the discrete random variable x. $\begin{array} { | c | c | c | c | c | c | } \hline x & 0 & 2 & 4 & 6 & 8 \\\hline p ( x ) & - .1 & .1 & .2 & .3 & .5 \\\hline\end{array}$

The rate of return for an investment can be described by a normal distribution with and standard deviation 3%. What is the probability that the rate of return for the investment will be at least 43.5%?

Explain why the following is or is not a valid probability distribution for the discrete random variable x. $\begin{array} { | c | c | c | c | c | c | } \hline x & 10 & 20 & 30 & 40 & 50 \\\hline p ( x ) & .3 & .2 & .2 & .2 & .2 \\\hline\end{array}$

Classify the following random variable according to whether it is discrete or continuous. The number of phone calls to the attendance office of a high school on any given school day

Classify the following random variable according to whether it is discrete or continuous. The blood pressures of a group of students the day before the final exam

Classify the following random variable according to whether it is discrete or continuous. The number of goals scored in a soccer game

The continuity correction factor is the name given to the .5 adjustment necessary when estimating the binomial with the normal distribution.

You test 3 items from a lot of 12. What is the probability that you will test no defective items if the lot contains 2 defective items?

A small life insurance company has determined that on the average it receives 5 death claims per day. Find the probability that the company receives at least seven death claims on a randomly selected day.

$\text { Compute } \left( \begin{array} { l } 4 \\4\end{array} \right)$

Consider the given discrete probability distribution. Find $P ( x < 2 \text { or } x > 3 ) \text {. }$ $\begin{array} { | c | c | c | c | c | c | } \hline x & 1 & 2 & 3 & 4 & 5 \\\hline p ( x ) & .1 & .2 & .2 & .3 & .2 \\\hline\end{array}$

The preventable monthly loss at a company has a normal distribution with a mean of $7800 standard deviation of $30. A new policy was put into place, and the preventable loss the next month was $7620. What inference can you make about the new policy?

$\begin{array}{l}\text { Consider the given discrete probability distribution. Find } P ( x \leq 4 ) \text {. }\\\begin{array} { | c | c | c | c | c | c | c | } \hline x & 0 & 1 & 2 & 3 & 4 & 5 \\\hline p ( x ) & .30 & .25 & .20 & .15 & .05 & .05 \\\hline\end{array}\end{array}$

The exponential distribution has the property that its mean equals its standard deviation.

Suppose the candidate pool for two appointed positions includes 6 women and 9 men. All candidates were told that the positions were randomly filled. Find the probability that two men are selected to fill the appointed positions.

Quiz 4: Random Variables and Probability Distributions

A certain baseball player hits a home run in 3% of his at-bats. Consider his at-bats as independent events. How many home runs do we expect the baseball player to hit in 600 at-bats?

The rate of return for an investment can be described by a normal distribution with and standard deviation 3%. What is the probability that the rate of return for the investment will be at least 43.5%?

Classify the following random variable according to whether it is discrete or continuous. The number of phone calls to the attendance office of a high school on any given school day

Classify the following random variable according to whether it is discrete or continuous. The blood pressures of a group of students the day before the final exam

Classify the following random variable according to whether it is discrete or continuous. The number of goals scored in a soccer game

The continuity correction factor is the name given to the .5 adjustment necessary when estimating the binomial with the normal distribution.

You test 3 items from a lot of 12. What is the probability that you will test no defective items if the lot contains 2 defective items?

A small life insurance company has determined that on the average it receives 5 death claims per day. Find the probability that the company receives at least seven death claims on a randomly selected day.

Compute (44) \text { Compute } \left( \begin{array} { l } 4 \\4\end{array} \right) Compute (44​)

The preventable monthly loss at a company has a normal distribution with a mean of $7800 standard deviation of $30. A new policy was put into place, and the preventable loss the next month was $7620. What inference can you make about the new policy?

The exponential distribution has the property that its mean equals its standard deviation.

Suppose the candidate pool for two appointed positions includes 6 women and 9 men. All candidates were told that the positions were randomly filled. Find the probability that two men are selected to fill the appointed positions.

$\text { Compute } \left( \begin{array} { l } 4 \\4\end{array} \right)$