Stats: Modeling the World Nasta Edition Grades 9-12
Stats: Modeling the World Nasta Edition Grades 9-12
3rd Edition
ISBN: 9780131359581
Author: David E. Bock, Paul F. Velleman, Richard D. De Veaux
Publisher: PEARSON
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Chapter 11, Problem 25E
To determine

To Calculate: In order to get a licence, the average number of tests drivers perform. A minimum of 20 runs should be used for simulations.

Expert Solution & Answer
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Explanation of Solution

34 percent is the number of applicants who first pass the driver's licence test.

The percentage of applicants not passing the driver's licence exam for the first time is 66 percent.

72 percent is the number of applicants who pass the exam on subsequent retests.

Thus, the proportion of applicants who pass the driver's licence exam the second time is

66x 0.72 = 47.52 = 47.52

= 48 percent

So, on the third test or the fourth test, the remaining candidates will pass the test, etc. The proportion of candidates on the third and subsequent tests who pass the test is,

(100-34-48) percent = 18%

Using two random digits to give 00-33 representing the first passing of the test, 34-81 representing the second passing of the test, and 82-99 representing the third and subsequent passing of the test.

In order to get a licence, the goal is to estimate the average number of tests drivers take.

It is equally possible that digits from 00 to 99 will occur.

Using Minitab, we have run 150 trials.

If the integer is between 00 and 33, we give a value of 1; a value of 2 if the integer is between 34 and 81; and a value of 3 if the integer is between 00 and 33.

Between 82 and 99 (with 3 or more tests indicated)

Answer variable overview statistics, Y (Number of tests) is,

    Random numberintegerNo. of tests to Pass
    11.215111
    50.45502
    84.5484843
    4.8548541
    32.33331
    71.54712
    80.25802
    74.22742
    14.523141
    65.54652
    24.69241
    30.854301
    81812
    78.25782
    30.01301
    98.2983
    23.12231
    52.882522
    22.145221
    52.84522
    41.52412
    65.995652
    14.21141
    18.254181
    39.55392
    86.87863
    37.845372
    17.586171
    65.54652
    42.36422

Mean = 1.7333 = 1.733

Median = 2

The Mode = 2

Based on this simulation, we predict that an average of 1.73 tests would need to be taken by drivers hoping to pass the licence exam.

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