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# Statistics : Distributions, Probability, Means, Medians, Quartiles and Five-Number Summary (13 Problems)

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1. The array below shows the number of days required for approval for
a random selection of small business loan applications:

56 21 38 17 15 67 45 48 60 56 22 53 37 17

50 92 39 16 59 73 17 31 28 51 74 42 31

What is the arithmetic mean for these observations? (Round the
calculation to two decimal places.)
a. 42.00
b. 42.78
c. 41.25
d. None of the above

2. Using the array in #1 above, calculate the median of the
distribution, rounding to two decimal places.
a. 42.00
b. 42.78
c. 41.25
d. None of the above

3. Using the array in question 1 above, calculate the arithmetic mean
with the single most extreme outlier removed. Round the
calculation to two decimal places.
a. 40.50
b. 40.89
c. 41.92
d. 43.85

4. The following is a five-number summary calculated from
observations of the percentage of calories that come from fat in 23
items advertised as "reduced" fat from a sample of fast food chain
restaurants. Form the box-and-whisker plot, select the phrase
below which bests describes the shape of the distribution.
__________________________________
| 15 | 20 | 22 | 26 | 30 |
|____ |______ |______ |_______|_______|

a. Skewed slightly to the left
b. Skewed slightly to the right
c. Symmetrical distribution
d. There is not enough information given to determine the shape

5. The following data represents the processing times required to pack
20 randomly selected computer hardware orders for mailing:

5.62 16.25 11.46 8.45 5.41 11.62 7.5 4.42 7.58 7.54

5.29 10.92 21.62 8.58 11.42 7.29 7.96 10.5 9.29 8.92

What is the third quartile?
a. 10.92
b. 11.05
c. 11.42
d. 11.46

6. What is the standard deviation of the distribution of the
observations in the array shown in question 11 above?
a. 0.894
b. 3.998
c. 4.199
d. 15.981

7. What is the coefficient of variation for the observations in the array
shown in question 11 above?
a. 39.97 %
b. 44.15%
c. 42.61%
d. 46.94 %

8. The employees of a company were surveyed on questions regarding
their educational background and marital status. Of the 600
employees, 400 had college degrees, 100 were single, and 60 were
single college graduates. The probability that an employee of the
company is married and has a college degree is:
a. 40/600
b. 340/600
c. 400/600
d. 500/600

9. An advertising executive is studying TV viewing habits of married
men and women during prime time hours. On the basis of past
viewing records, the executive has determined that during prime
time, husbands are watching TV 60% of the time that their wives
are also watching TV. When the husband is not watching TV, 30%
of the time his wife is watching TV. What is the probability that, if
the wife is watching TV, her husband is also watching TV?
a. 0.12
b. 0.24
c. 0.36
d. 0.67

10. Mothers Against Drunk Driving is a very visible group whose main
focus is to educate the public about the harm caused by drunk
drivers. A study was recently done that emphasized the problem we
all face with drinking and driving. Four hundred accidents that
occurred on a Saturday night were analyzed. Two items noted were
the number of vehicles involved and whether alcohol played a role in
the accident. The numbers are shown below:

Number of vehicles Involved
Did alcohol play a role? 1 2 3 Totals
Yes 50 100 20 170
No 25 175 30 230 1
Totals 75 275 50 400

Referring to the table above, what proportion of accidents involved
more than one vehicle?
a. 50/400
b. 75/400
c. 275/400
d. 325/400

11. Referring to the table in question 20 above, what proportion of the
non-alcohol related accidents were multiple vehicle accidents?
a. 50/170
b. 120/170
c. 205/230
d. 25/230

12. A company has 2 machines that produce widgets. An older machine
produces 23% defective widgets, while the new machine produces
only 8% defective widgets. In addition, the new machine produces 3
times as many widgets as the older machine does. What is the
probability that a randomly chosen widget produced by the company
is defective?
a. .055
b. .0775
c. .1175
d. .256

13. A survey is taken among customers of a fast-food restaurant to
determine preference for hamburger or chicken. Of 200 respondents
selected, 75 were children and 125 were adults. 120 preferred
hamburger and 80 preferred chicken. 55 of the children preferred
hamburger. What is the probability that a randomly selected
a. 0.50
b. 0.625
c. 0.75
d. None of the above

##### Solution Summary

Thirteen Statistics problems involving Distributions, Probability, Means, Quartiles and Five Number Summary are solved. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

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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