# Project #2795 - Data Description and Probability Distribution

1. (8 pts) Find the median of the following data.  (no work/explanation required)    1.  ____D______

53       49        60        77        88        48        77        37        33

A.   53

B.   58

C.   77

D.   88

2. (18 pts) The mileages of 30 cars were compiled (in miles per gallons):

35        29        37        30        32        44        29        42        27        30

26        20        36        19        29        28        20        24        25        37

40        27        28        18        41        22        18        37        38        43

Summarize the data by constructing a frequency distribution and a relative frequency distribution, using intervals shown below. (Fill in the table.)

 Mileage (miles per gallon) Frequency Relative Frequency (to the nearest thousandth) 14.5 –    19.5 19.5 –    24.5 24.5 –    29.5 29.5 –    34.5 34.5 –    39.5 39.5 –    44.5 Total

Consider the following table and pie chart for #3.

Assume that the values in the given table are correct.

Major         Number           %

of Seniors      of Seniors

Computer Sci.     194           10

English                 236           12

Biology                134             7

Psychology            40             2

Other majors       681           36

Total Number

of Seniors          1918         100

3. (8 pts) Which of the following best describes the most serious problem with the pie chart?

(no explanation required)                                                                                              3. _______

A. The sizes of the pie wedges are incorrect because the business wedge is too large and the English wedge is too small.

B. The sizes of all the pie wedges are incorrect because an additional wedge must be included.

C. The numbers shown in the pie chart for the selected majors do not match the numbers in the % column of the table for those selected majors.

D. The numbers in the pie chart should be followed by “%” because the values are percentages.

4. (32 pts)  The number of calories per hot dog was determined for 10 brands of poultry hot dogs. The data are

162       97         84         100       145       130       95         155       95         177

(a) Find the median. Show some work/explanation.

(b) State the mode(s).

(c) Compute the sample mean, the sample variance, and the sample standard deviation.

Use the table below to help organize your work. Fill in the table.

 xi 162 97 84 100 145 130 95 155 95 177 Total: _____ Total:  _____ Total: ______

Mean  = _________

Sample Variance = _____________

Standard Deviation= _____________

(d) What percentage of the data fall within one standard deviation of the mean? Show work/explanation.

5. (12 pts)  Exam scores. Find the mean for the grouped data in the following table. Show work. (Extra space provided in table for scratch work.)

 40 Exam Scores Interval Frequency 49.5 - 59.5 6 59.5 - 69.5 12 69.5 - 79.5 10 79.5 - 89.5 8 89.5 - 99.5 4

6. (22 pts) A particular basketball player makes a free throw with probability 0.72

(Report answers rounded to four decimal places. Show work.)

(a) What is the probability that out of six free throws, the player makes exactly four of them?

Show work.

(b) What is the probability that out of six free throws, the player makes all six of them?

Show some work/explanation.

(c) What is the probability that out of six free throws, the player does not make any of them? Show some work/explanation.

(d) What is the probability that out of six free throws, the player makes at least one of them?

Show some work/explanation.

 Subject Mathematics Due By (Pacific Time) 03/03/2013 03:00 pm
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