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# Probability

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Question 1 (5 points)
Chose a simple random sample of size five (5) from the following employees of a small company.

1. Bechhofer 4. Kesten 7. Taylor
2. Brown 5. Kiefer 8. Wald
3. Ito 6. Spitzer 9. Weiss

Use the numerical labels attached to the names above and the following list of random digits. Read the list of random digits from left to right, starting at the beginning of the list.

11003 20131 05907 11384 44982 20751 27498 12009 45287

The simple random sample is

a. Bechhofer, Brown, Ito, Kiefer, and Weiss.
b. Bechhofer, Ito, Kiefer, Taylor, and Weiss.
c. Bechhofer, Brown, Ito, Kesten, and Wald.
d. Brown, Ito, Kesten, Spitzer, and Wald.

Question 2 (5 points)
A survey conducted by Black Flag asked whether the action of a certain type of roach disk would be effective in killing roaches. 79 percent of the respondents agreed that the roach disk would be effective. The outcome, 79 percent, is a

a. sample space.
b. simple outcome.
c. statistic.
d. synonym.

Question 3 (5 points)
The experiment is to roll a six-sided die and to observe which side comes up. The collection of specific outcomes that could occur as a result of the experiment is known as the

a. an event.
b. simple outcome.
c. statistic.
d. synonym.

Question 4 (6 points)
You have a vase that contains 5 red, 4 white, and 3 blue marbles. You reach into the vase a draw a marble. What is the probability that the marble selected is white [P(W)]?

a. 0.5833
b. 0.4167
c. 0.3333
d. 0.25

Question 5 (6 points)
The experiment is to pick a card from a deck of ten (10) cards, numbered 1 through 10, and flip a two-sided coin labeled "heads" on one side "tails" on the other.

Event A represents observing an even numbered card.
Event B represends observing a "head" on the coin.

What is the probability that event A and B occur as a result of the experiment?

a. 0.2500
b. 0.5000
c. 0.7500
d. 1.0000

Question 6 (6 points)
You have a vase that contains 5 red, 4 white, and 3 blue marbles. You reach into the vase a draw a marble. What is the probability that the marble selected is red and white [P(R and W)]?

a. 0.0000
b. 0.2500
c. 0.3333
d. 0.4167

Question 7 (5 points)
You have a deck of cards numbered 1 through 10. You select a card. What is the probability that the card selected has an odd number or a number less than 6 [P(O or <6)]?

a. 0.2500
b. 0.5000
c. 0.7000
d. 1.0000

Question 8 (6 points)
You have a deck of cards numbered 1 through 10. You select a card. What is the probability that the card selected has an odd number and a number less than 6 [P(O and <6)]?

a. 0.0000
b. 0.2500
c. 0.3000
d. 0.7000

Question 9 (6 points)
As NCAA investigators continue to probe deeper into college sports, an offical indicates that 70 percent of collegiate basketball programs violate NCAA rules. Out of 40 programs examined this year, what is the probaility that at least 80 percent have committed rule violations [P( &#8805; 80%)]?

a. 0.0838
b. 0.5838
c. 0.8000
d. 0.9162

Question 10 (6 points)

The ABC Company has manufactured light bulbs for the last 75 years. During this time the company has established a defective rate of 10%. As part of the quality control process random samples of 50 light bulbs are selected for testing.

What is the probability that at least 5% of the light bulbs are defective [P( &#8805; 5%)]?

a. 0.1193
b. 0.3333
c. 0.8807
d. 1.0000

Question 11 (6 points)
As NCAA investigators continue to probe deeper into college sports, an offical indicates that 70 percent of collegiate basketball programs violate NCAA rules. Out of 40 programs examined this year, what is the probaility that the proportion of program committing rule violations this year will exceed the norm by at least 5 percent [P( - p &#8805; 5%)]?

a. 0.2451
b. 0.4902
c. 0.7451
d. none of the above

Question 12 (10 points)
As NCAA investigators continue to probe deeper into college sports, an offical indicates that 70 percent of collegiate basketball programs violate NCAA rules. Out of 40 programs examined this year, what is the probaility that no more than 25 percent have committed rule violations [P( &#8804; 25%)]?

a. 1.0000
b. 0.7500
c. 0.3333
d. 0.0000

Question 13 (6 points)

The scores of students on the ACT college entrance examination in a recent year had a normal distribution with a mean &#956; = 18.6 and standard deviation &#963; = 5.9.

If a random sample of 400 students was drawn, what is the probability that the sample mean () will be at least 21 [P( &#8805; 21)]?

a. 0.0000
b. 0.3750
c. 0.6250
d. 1.0000

Question 14 (6 points)
Fortune Magazine reported that the impact of leveraged buyouts is difficult to detect. In 1998 the average value of "Fortune 500" firms who were bought out was \$3.75 billion with a standard deviation of \$1.92 billion. If a sample of 64 firms is taken from the "Fortune 500" firms, what is the probability that the sample mean is determined to be between \$3.5 and \$4.5 billion [P(\$3.5 billion &#8804; &#8804; \$4.5 billion)]?

a. 0.8503
b. 0.8499
c. 0.3503
d. 0.2479

Question 15 (6 points)

The scores of students on the ACT college entrance examination in a recent year had a normal distribution with a mean &#956; = 18.6 and standard deviation &#963; = 5.9.

If a random sample of 400 students was drawn, what is the probability that the sample mean () will not exceed 17 [P( &#8804; 17)]?

a. 0.0000
b. 0.0762
c. 0.9238
d. 1.0000

Question 16 (10 points)

The scores of students on the ACT college entrance examination in a recent year had a normal distribution with a mean &#956; = 18.6 and standard deviation &#963; = 5.9.

If a random sample of 400 students was drawn, what is the probability that the sample mean () will exceed the norm by at least 2 points [P( - &#956; &#8805; 2)]?

a. 0.0000
b. 0.2513
c. 0.6778
d. 1.0000

##### Solution Summary

Question 1 (5 points)
Chose a simple random sample of size five (5) from the following employees of a small company.

1. Bechhofer 4. Kesten 7. Taylor
2. Brown 5. Kiefer 8. Wald
3. Ito 6. Spitzer 9. Weiss

Use the numerical labels attached to the names above and the following list of random digits. Read the list of random digits from left to right, starting at the beginning of the list.

11003 20131 05907 11384 44982 20751 27498 12009 45287

The simple random sample is

a. Bechhofer, Brown, Ito, Kiefer, and Weiss.
b. Bechhofer, Ito, Kiefer, Taylor, and Weiss.
c. Bechhofer, Brown, Ito, Kesten, and Wald.
d. Brown, Ito, Kesten, Spitzer, and Wald.

Question 2 (5 points)
A survey conducted by Black Flag asked whether the action of a certain type of roach disk would be effective in killing roaches. 79 percent of the respondents agreed that the roach disk would be effective. The outcome, 79 percent, is a

a. sample space.
b. simple outcome.
c. statistic.
d. synonym.

Question 3 (5 points)
The experiment is to roll a six-sided die and to observe which side comes up. The collection of specific outcomes that could occur as a result of the experiment is known as the

a. an event.
b. simple outcome.
c. statistic.
d. synonym.

Question 4 (6 points)
You have a vase that contains 5 red, 4 white, and 3 blue marbles. You reach into the vase a draw a marble. What is the probability that the marble selected is white [P(W)]?

a. 0.5833
b. 0.4167
c. 0.3333
d. 0.25

Question 5 (6 points)
The experiment is to pick a card from a deck of ten (10) cards, numbered 1 through 10, and flip a two-sided coin labeled "heads" on one side "tails" on the other.

Event A represents observing an even numbered card.
Event B represends observing a "head" on the coin.

What is the probability that event A and B occur as a result of the experiment?

a. 0.2500
b. 0.5000
c. 0.7500
d. 1.0000

Question 6 (6 points)
You have a vase that contains 5 red, 4 white, and 3 blue marbles. You reach into the vase a draw a marble. What is the probability that the marble selected is red and white [P(R and W)]?

a. 0.0000
b. 0.2500
c. 0.3333
d. 0.4167

Question 7 (5 points)
You have a deck of cards numbered 1 through 10. You select a card. What is the probability that the card selected has an odd number or a number less than 6 [P(O or <6)]?

a. 0.2500
b. 0.5000
c. 0.7000
d. 1.0000

Question 8 (6 points)
You have a deck of cards numbered 1 through 10. You select a card. What is the probability that the card selected has an odd number and a number less than 6 [P(O and <6)]?

a. 0.0000
b. 0.2500
c. 0.3000
d. 0.7000

Question 9 (6 points)
As NCAA investigators continue to probe deeper into college sports, an offical indicates that 70 percent of collegiate basketball programs violate NCAA rules. Out of 40 programs examined this year, what is the probaility that at least 80 percent have committed rule violations [P( &#8805; 80%)]?

a. 0.0838
b. 0.5838
c. 0.8000
d. 0.9162

Question 10 (6 points)

The ABC Company has manufactured light bulbs for the last 75 years. During this time the company has established a defective rate of 10%. As part of the quality control process random samples of 50 light bulbs are selected for testing.

What is the probability that at least 5% of the light bulbs are defective [P( &#8805; 5%)]?

a. 0.1193
b. 0.3333
c. 0.8807
d. 1.0000

Question 11 (6 points)
As NCAA investigators continue to probe deeper into college sports, an offical indicates that 70 percent of collegiate basketball programs violate NCAA rules. Out of 40 programs examined this year, what is the probaility that the proportion of program committing rule violations this year will exceed the norm by at least 5 percent [P( - p &#8805; 5%)]?

a. 0.2451
b. 0.4902
c. 0.7451
d. none of the above

Question 12 (10 points)
As NCAA investigators continue to probe deeper into college sports, an offical indicates that 70 percent of collegiate basketball programs violate NCAA rules. Out of 40 programs examined this year, what is the probaility that no more than 25 percent have committed rule violations [P( &#8804; 25%)]?

a. 1.0000
b. 0.7500
c. 0.3333
d. 0.0000

Question 13 (6 points)

The scores of students on the ACT college entrance examination in a recent year had a normal distribution with a mean &#956; = 18.6 and standard deviation &#963; = 5.9.

If a random sample of 400 students was drawn, what is the probability that the sample mean () will be at least 21 [P( &#8805; 21)]?

a. 0.0000
b. 0.3750
c. 0.6250
d. 1.0000

Question 14 (6 points)
Fortune Magazine reported that the impact of leveraged buyouts is difficult to detect. In 1998 the average value of "Fortune 500" firms who were bought out was \$3.75 billion with a standard deviation of \$1.92 billion. If a sample of 64 firms is taken from the "Fortune 500" firms, what is the probability that the sample mean is determined to be between \$3.5 and \$4.5 billion [P(\$3.5 billion &#8804; &#8804; \$4.5 billion)]?

a. 0.8503
b. 0.8499
c. 0.3503
d. 0.2479

Question 15 (6 points)

The scores of students on the ACT college entrance examination in a recent year had a normal distribution with a mean &#956; = 18.6 and standard deviation &#963; = 5.9.

If a random sample of 400 students was drawn, what is the probability that the sample mean () will not exceed 17 [P( &#8804; 17)]?

a. 0.0000
b. 0.0762
c. 0.9238
d. 1.0000

Question 16 (10 points)

The scores of students on the ACT college entrance examination in a recent year had a normal distribution with a mean &#956; = 18.6 and standard deviation &#963; = 5.9.

If a random sample of 400 students was drawn, what is the probability that the sample mean () will exceed the norm by at least 2 points [P( - &#956; &#8805; 2)]?

a. 0.0000
b. 0.2513
c. 0.6778
d. 1.0000

Solution provided by:
###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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