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# Descriptive Statistics & Normal Probability

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See attached Minitab sheet for use with one of the questions.

Please us either Excel or Minitab to answer the questions, where necessary

1. The following information regarding the top eight Fortune 500 companies was presented in a recent issue of Fortune Magazine.

Sales Sales Profits Profits
Company \$ Millions Rank \$ Millions Rank

General Motors 161,315 1 2,956 30
Ford Motor 144,416 2 22,071 2
Wal-Mart Stores 139,208 3 4,430 14
Exxon 100,697 4 6,370 5
General Electric 100,469 5 9,269 3
Int'l Business Machines 81,667 6 6,328 6
Citigroup 76,431 7 5,807 8
Philip Morris 57,813 8 5,372 9
Boeing 56,154 9 1,120 82
AT&T 53,588 10 6,398 4

a. How many variables are in this data set?
b. How many observations are in this data set?
c. Which variables are qualitative and which are quantitative variables?
d. What measurement scale is used for each variable?

2. Thirty students in the School of Business were asked what their majors were. The following represents their responses (M = Management; A = Accounting;
E = Economics; O = Others).

A M M A M M E M O A
E E M A O E M A M A
M A O A M E E M A M

a. Construct a frequency distribution.
b. Construct a bar chart.
c. Construct a relative frequency distribution.
d. Construct a pie chart.

3. A private research organization studying families in various countries reported the following data for the amount of time 4-year old children spent alone with their fathers each day.

Time with

Belgium 30
China 40
Finland 48
Germany 37
Nigeria 42
Sweden 46
U.S. 47
Brazil 34
Costa Rica 46
Mexico 43
South Korea 32

a. Compute the sample mean.
b. Compute the median
c. Compute the mode
d. Compute the sample variance.
e. Compute the sample Std. Dev. (Give your interpretation of the Std. Dev.)
f. Determine the 25th percentile.
g. Determine the 75th percentile.
h. Determine the interquartile range.
i. Although there are only 15 numbers, is there any indication from your answers in a, b, and c, as to whether the distribution of this set of numbers is skewed or not? If so, why and which way is it skewed?

4. Attached is a MINITAB spreadsheet containing information on 40 NFL players. Use the information to answer the following questions.
a. Create a histogram and a dot plot of the 'weight' data, and common shape of the sample data.
b. From the histogram, about how many players are near the mean weight?
c. Use MINITAB to calculate the standard deviation. Why do you think it is so large?

5. The time it takes to hand carve a guitar neck is uniformly distributed between 110 and 190 minutes.

a. What is the probability that a guitar neck can be carved between 115 and 165 minutes?
b. What is the probability that the guitar neck can be carved in exactly 120 minutes?
c. Determine the expected completion time for carving the guitar neck.
d. Compute the standard deviation.

6. Scores on a recent national statistics exam were normally distributed with a mean of 80 and a standard deviation of 6.

a. What is the probability that a randomly selected exam will have a score of at least 71?
b. What percentage of exams will have scores between 89 and 92?
c. If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award?
d. If there were 334 exams with scores of at least 89, how many students took the exam?
e. What are the minimum and the maximum scores of the middle (75%) of the graduates?

7. A major department store has determined that its customers charge an average of \$500 per month, with a standard deviation of \$80. Assume the amounts of charges are normally distributed.

a. What percentage of customers charges more than \$380 per month?
b. What percentage of customers charges between \$644 and \$700 per month?
c. Ninety percent of the customers will charge at least how many dollars per month?

8. The life expectancy in the United States is 75 with a standard deviation of 6 years. A random sample of 36 individuals is selected.
a. What is the mean, standard deviation and shape of this sampling distribution?
b. What is the probability that the sample mean will be between 72 and 75 years?
c. What is the probability that the sample mean will be larger than 73.46 years?

9. A random sample of n=100 observations is selected from a population with
m =100 and s=10.
a. What are the largest and smallest values that you would expect to see in the 100 observations?
b. Although we would expect the mean of the means to be equal to the mean of the individuals, but due to random variation it is unlikely that the two would actually be the same. So, how far, at most, would you expect the mean of the 100 observations to be from µ?

10. Describe the three things that the Central Limit Theorem tells us about the sampling distribution.
a.
b.
c.