Question 1

For a binomial experiment, the probability of success is 40% and the number of trials is 5. Let X represent the number of successes.
-Find the P(X = 2).

Accepted Answer

The answer of For a binomial experiment, the probability of...

Question 2

If the probability distribution of X is:
$$\begin{array} { c c } 
\mathrm { X } & \mathrm { P } ( \mathrm { X } ) \
3 & 1 / 8 \
4 & 1 / 8 \
5 & 3 / 8 \
6 & 3 / 8
\end{array}$$
-What is the expected value of X?

Accepted Answer

A) 1 
B) 2 
C) 3 
D) 4 
E) 5

Question 3

During off hours, cars arrive at a highway service station at an average rate of 0.5 cars per minute. The arrivals are distributed according to the Poisson distribution.
-What is the probability that during the next minute three cars will arrive?

Accepted Answer

The answer of During off hours, cars arrive at a...

Question 4

A car wash loses $30 on rainy days and makes $120 on days when is does not rain.If the probability of rain is 0.15,calculate the car wash's expected profit.

Accepted Answer

The answer of A car wash loses $30 on rainy...

Question 5

An urn contains 50 black balls and 20 blue balls.If you select 30 balls at random,what is the standard deviation of the number of black balls?

Accepted Answer

A) 3.55 
B) 1.88 
C) 4.24 
D) 2.85 
E) 4.62

Question 6

In the most recent students' council election, 19% of all eligible university students voted. If a random sample of 20 students were surveyed at the university:
-Find the probability that exactly half voted in the election.

Accepted Answer

A) 0.0000 
B) 0.0014 
C) 0.0148 
D) 0.2500 
E) 0.4997

Question 7

The mean of the binomial distribution is equal to:

Accepted Answer

A) p 
B) np 
C) px(1 - p)n-x 
D) npq 
E)  $\sqrt { n p q }$

Question 8

Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads).
-Determine the expected number of heads.

Accepted Answer

The answer of Consider the experiment of tossing a fair...

Question 9

Find the premium that the insurance company should charge if it wants its expected net profit to be $2000?
-Find the premium that the insurance company should charge if it wants its expected net profit to be $2000?

Accepted Answer

The answer of Find the premium that the insurance company...

Question 10

Whenever p = .5,the binomial distribution will _________ be symmetric.

Accepted Answer

A) always 
B) sometimes 
C) never

Question 11

According to company records at a large firm,40% of all employees have a university degree.If six employees were selected at random from the company,what is the probability that none of the six has a university degree?

Accepted Answer

A) 0002 
B) 0243 
C) 0378 
D) 0467 
E) 0697

Question 12

A lawyer believes that the probability is .3 that she can win a discrimination suit.If she wins the case she will make $40,000,but if she loses she gets nothing.Assume that she has to spend $5000 preparing the case.What is her expected gain?

Accepted Answer

The answer of A lawyer believes that the probability is...

Question 13

During off hours, cars arrive at a highway service station at an average rate of 0.5 cars per minute. The arrivals are distributed according to the Poisson distribution.
-What is the probability that during the next five minutes three cars will arrive?

Accepted Answer

The answer of During off hours, cars arrive at a...

Question 14

The mean of the binomial distribution with n trials and probability of success p is np(1 - p).

Accepted Answer

A) True 
 B)False

Question 15

In the most recent students' council election, 19% of all eligible university students voted. If a random sample of 20 students were surveyed at the university:
-Find the probability that none of the students voted.

Accepted Answer

A) 0.0000 
B) 0.0014 
C) 0.0148 
D) 0.2500 
E) 0.4997

Question 16

If n = 15 and p = .4,then the standard deviation of the binomial distribution is

Accepted Answer

A) 9 
B) 6 
C) 3.6 
D) 1.8974 
E) 4

Question 17

If p = .5 and n = 4,then the corresponding binomial distribution is _____.

Accepted Answer

A) right skewed 
B) left skewed 
C) symmetric 
D) bimodal 
E) multimodal

Question 18

According to a survey of adults,64% have money in a regular savings account independent of other adults.If we plan on surveying 50 randomly selected adults,find the mean number of adults who would have regular savings accounts.

Accepted Answer

A) 12 
B) 22 
C) 32 
D) 42 
E) 46

Question 19

Find the probability of 10 customers or less arriving within a minute.

Accepted Answer

The answer of Find the probability of 10 customers or...

Question 20

The J.O. Supplies Company buys calculators from a foreign supplier. The probability of a defective calculator is 10%.
-If 10 calculators are selected at random,what is the probability that 3 or more of the calculators will be defective?

Accepted Answer

The answer of The J.O. Supplies Company buys calculators from...

Exam 4: Discrete Random Variables

For a binomial experiment, the probability of success is 40% and the number of trials is 5. Let X represent the number of successes. -Find the P(X = 2).

If the probability distribution of X is: $\begin{array} { c c } \mathrm { X } & \mathrm { P } ( \mathrm { X } ) \\3 & 1 / 8 \\4 & 1 / 8 \\5 & 3 / 8 \\6 & 3 / 8\end{array}$ -What is the expected value of X?

During off hours, cars arrive at a highway service station at an average rate of 0.5 cars per minute. The arrivals are distributed according to the Poisson distribution. -What is the probability that during the next minute three cars will arrive?

A car wash loses $30 on rainy days and makes $120 on days when is does not rain.If the probability of rain is 0.15,calculate the car wash's expected profit.

An urn contains 50 black balls and 20 blue balls.If you select 30 balls at random,what is the standard deviation of the number of black balls?

In the most recent students' council election, 19% of all eligible university students voted. If a random sample of 20 students were surveyed at the university: -Find the probability that exactly half voted in the election.

The mean of the binomial distribution is equal to:

Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads). -Determine the expected number of heads.

Find the premium that the insurance company should charge if it wants its expected net profit to be $2000? -Find the premium that the insurance company should charge if it wants its expected net profit to be $2000?

Whenever p = .5,the binomial distribution will _________ be symmetric.

According to company records at a large firm,40% of all employees have a university degree.If six employees were selected at random from the company,what is the probability that none of the six has a university degree?

A lawyer believes that the probability is .3 that she can win a discrimination suit.If she wins the case she will make $40,000,but if she loses she gets nothing.Assume that she has to spend $5000 preparing the case.What is her expected gain?

During off hours, cars arrive at a highway service station at an average rate of 0.5 cars per minute. The arrivals are distributed according to the Poisson distribution. -What is the probability that during the next five minutes three cars will arrive?

The mean of the binomial distribution with n trials and probability of success p is np(1 - p).

In the most recent students' council election, 19% of all eligible university students voted. If a random sample of 20 students were surveyed at the university: -Find the probability that none of the students voted.

If n = 15 and p = .4,then the standard deviation of the binomial distribution is

If p = .5 and n = 4,then the corresponding binomial distribution is _____.

According to a survey of adults,64% have money in a regular savings account independent of other adults.If we plan on surveying 50 randomly selected adults,find the mean number of adults who would have regular savings accounts.

Find the probability of 10 customers or less arriving within a minute.

The J.O. Supplies Company buys calculators from a foreign supplier. The probability of a defective calculator is 10%. -If 10 calculators are selected at random,what is the probability that 3 or more of the calculators will be defective?

Exam 4: Discrete Random Variables

For a binomial experiment, the probability of success is 40% and the number of trials is 5. Let X represent the number of successes. -Find the P(X = 2).

If the probability distribution of X is: XP(X) 31/841/853/863/8\begin{array} { c c } \mathrm { X } & \mathrm { P } ( \mathrm { X } ) \\3 & 1 / 8 \\4 & 1 / 8 \\5 & 3 / 8 \\6 & 3 / 8\end{array}X3456​P(X) 1/81/83/83/8​ -What is the expected value of X?

During off hours, cars arrive at a highway service station at an average rate of 0.5 cars per minute. The arrivals are distributed according to the Poisson distribution. -What is the probability that during the next minute three cars will arrive?

A car wash loses $30 on rainy days and makes $120 on days when is does not rain.If the probability of rain is 0.15,calculate the car wash's expected profit.

An urn contains 50 black balls and 20 blue balls.If you select 30 balls at random,what is the standard deviation of the number of black balls?

In the most recent students' council election, 19% of all eligible university students voted. If a random sample of 20 students were surveyed at the university: -Find the probability that exactly half voted in the election.

The mean of the binomial distribution is equal to:

Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads). -Determine the expected number of heads.

Find the premium that the insurance company should charge if it wants its expected net profit to be $2000? -Find the premium that the insurance company should charge if it wants its expected net profit to be $2000?

Whenever p = .5,the binomial distribution will _________ be symmetric.

According to company records at a large firm,40% of all employees have a university degree.If six employees were selected at random from the company,what is the probability that none of the six has a university degree?

A lawyer believes that the probability is .3 that she can win a discrimination suit.If she wins the case she will make $40,000,but if she loses she gets nothing.Assume that she has to spend $5000 preparing the case.What is her expected gain?

During off hours, cars arrive at a highway service station at an average rate of 0.5 cars per minute. The arrivals are distributed according to the Poisson distribution. -What is the probability that during the next five minutes three cars will arrive?

The mean of the binomial distribution with n trials and probability of success p is np(1 - p).

In the most recent students' council election, 19% of all eligible university students voted. If a random sample of 20 students were surveyed at the university: -Find the probability that none of the students voted.

If n = 15 and p = .4,then the standard deviation of the binomial distribution is

If p = .5 and n = 4,then the corresponding binomial distribution is _____.

According to a survey of adults,64% have money in a regular savings account independent of other adults.If we plan on surveying 50 randomly selected adults,find the mean number of adults who would have regular savings accounts.

Find the probability of 10 customers or less arriving within a minute.

The J.O. Supplies Company buys calculators from a foreign supplier. The probability of a defective calculator is 10%. -If 10 calculators are selected at random,what is the probability that 3 or more of the calculators will be defective?

If the probability distribution of X is: $\begin{array} { c c } \mathrm { X } & \mathrm { P } ( \mathrm { X } ) \\3 & 1 / 8 \\4 & 1 / 8 \\5 & 3 / 8 \\6 & 3 / 8\end{array}$ -What is the expected value of X?