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Some MCQs on statistics

1. Binomial Distribution
A fair die is rolled nine times. What is the probability that an odd number (1,3 or 5) will occur less than 3 times?
a) .0899
b) .2544
c) .7456
d) .9101

4. Binomial Distribution
This problem is a modified version of problem 8 in chapter 11. An automaker has issued a recall for truck transmissions. It has found 30% of its transmissions to be defective, and has issued a recall asking consumers to take their truck to their dealer. The Friendly Auto Mart sold 10 of these trucks, but has only 3 transmissions in stock. What is the probability that the auto dealer will need to order more transmissions? You should take your calculations to 4 decimal places.
a) .2335
b) .3504
c) .3838
d) .6496

5. Normal Distribution
The metropolitan airport commission is considering the establishment of limitations on noise pollution around a local airport. At the present time, the noise level per jet takeoff in one neighborhood near the airport is approximately normally distributed with a mean of 100 decibels and a standard deviation of 3 decibels. What is the probability that a randomly selected jet will generate a noise level of more than 105 decibels?
a) 0.0228
b) 0.0475
c) 0.0485
d) 0.0500

7. Decision Making without Probability (10.0 points)
The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code.

If he uses the maximin criterion, how many new workers will he hire?
a) 1
b) 2
c) 3

9. Decision Tree Calculations
Consider the following decision tree.

What is the value associated with node 3?
a) 600
b) 1600
c) 1800
d) 2500

13. Random Number Generation

If a simulation begins with the first random number, what would the first simulation value be? (Hint: The random numbers are chosen from 0 - 100 with uniform distribution, so divide each random number by 100.)
a) 1
b) 2
c) 3
d) 4

14. Random Number Generation
Given this frequency distribution, the random number 0.61 would be interpreted as a demand of:

a) 0
b) 1
c) 2
d) 3

18. Moving Average Method
The following data summarizes the historical demand for a product

Determine the average forecast error when using the 4-month moving average method.
a) 5.25
b) 5.75
c) 6.25
d) 6.75

23. Consider the following graph of sales.

Which of the following characteristics is exhibited by the data?
a) Trend only
b) Seasonal only
c) Trend plus seasonal
d) Trend plus random

26. Consider the following annual sales data for 1996-2003, use the linear regression method and determine the estimated sales equation,

NOTE: This question was taken from a test bank and the test publisher did not use the actual year as the x-value. You should replace 1996 with 1, 1997 with 2, 1998 with 3, and so on. These x-values will lead you to the correct answer. This technique is also commonly used in real world examples.
a) y = 2.63 + 0.21x
b) y = 2.63 - 0.21x
c) y = -0.21 + 2.63x
d) y = 0.21 - 2.63x

27.Consider the following annual sales data for 1996-2003. This is the same table of data shown on the previous question. Again, please replace 1996 with 1, 1997 with 2, 1998 with 3, etc.
Using year values of 1 through 8 instead of 1996 through 2003, determine the percent of variation of sales that is caused by the year number (1-8). The answers below are rounded to the nearest tenth, but are far enough apart so your correct answer will be close to only one answer below.

a) 91.54%
b) 93.22%
c) 95.34%
d) 96.55%

28. The law firm of Dewey, Cheetham, and Howe has a pool of candidates wishing for internship in the law firm. The law firm has decided to test each candidate on his or her ability to win a nuisance lawsuit. Candidates who score in the top 33% will be given an internship. The law firm has issued similar tests in the past and knows that the average score is 80 (out of 100), the standard deviation is 10, and that test scores are normally distributed. What is the minimum score that a candidate must earn in order to place in the top 33%?
a) 81.25
b) 84.40
c) 86.30
d) 88.60

30. This question requires some thought, but the correct answer can be reached if you think long enough about it.
You are performing an analysis of your chosen forecasting method and have tracked errors for forecasts over the previous 24 time periods. You have obtained the following results from your error analysis:
MAD = 25
MAPD = 0.10
E (Cumm. error) = 5
What might you conclude about your forecasts?
a) Forecasts are consistently above the actual demand.
b) Forecasts are consistently below the actual demand.
c) Forecasts fluctuate wildly above and below the actual demand.

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Hi

Please find attached the answers with explainations for your questions.

I am not able to attach files so i am pasting the word file here. You will get answers to the questions here. I am sending the files to Brainmass so that they can forward the files to you.

Regards

Unless otherwise instructed, you should carry your calculations to 4 decimal places and then round your answer accordingly. Note that round-off errors can still occur, even if you are doing the problem correctly. This may result in your answer being 0.01, 0.001, or 0.0001 off the actual correct answer. Do not panic if this is the case. The multiple-choice answers are far enough apart that the closest answer should be obvious.

For your decision analysis questions, please make sure you know the difference between expected value GIVEN perfect information and expected value OF perfect information.

1. Binomial Distribution
A fair die is rolled nine times. What is the probability that an odd number (1,3 or 5) will occur less than 3 times?
a) .0899
b) .2544
c) .7456
d) .9101
In Binomial Distribution, Probability of r successes in n trials is given as:
P(r)=P(r)=nCr p^r *q^(n-r)
nCr= nCr= n!/r!(n-r)!
p = probability of a success=0.5
q = 1- p = probability of a failure=0.5
n = number of trials=9
r = number of successes in n trials

P(r<3)=P(r=0)+p(r=1)+P(r=2)
P(r=0)=9C0 (0.5)^0 (0.5)^9 =0.00195
P(r=1)=9C1 (0.5)^1 (0.5)^8 =0.0176
P(r=2)=9C2 (0.5)^2 (0.5)^7 =0.0703
Thus, P(r<3)=0.00195+0.0176+0.0703=0.08984
Thus, answer (a)

4. Binomial Distribution
This problem is a modified version of problem 8 in chapter 11. An automaker has issued a recall for truck transmissions. It has found 30% of its transmissions to be defective, and has issued a recall asking consumers to take their truck to their dealer. The Friendly Auto Mart sold 10 of these trucks, but has only 3 transmissions in stock. What is the probability that the auto dealer will need to order more transmissions? You should take your calculations to 4 decimal places.
a) .2335
b) .3504
c) .3838
d) .6496

P(r)=nCr p^r *q^(n-r)
nCr= n!/r!(n-r)!
p = probability of a ...

Solution Summary

This posting contains solutions to following MCQs.

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