Chapter 11, Problem 26E

To determine

To Calculate: The number of those checked who, after two tries, still do not have a driver's licence.

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)

Random number	integer	No. of tests to Pass
11.215	11	1
50.45	50	2
84.5484	84	3
4.85485	4	1
83.54	83	3
71.54	71	2
80.25	80	2
74.22	74	2
14.523	14	1
65.54	65	2
24.69	24	1
30.854	30	1
81	81	2
78.25	78	2
30.01	30	1
98.2	98	3
23.12	23	1
52.882	52	2
22.145	22	1
52.84	52	2
41.52	41	2
65.995	65	2
14.21	14	1
18.254	18	1
39.55	39	2
86.87	86	3
37.845	37	2
17.586	17	1
65.54	65	2
42.36	42	2

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

The number of times we get "3" = 4 is obtained from the simulation trials

Thus, the percentage of those tested who still do not have a driver's licence after two attempts is based on this simulation.

  $\begin{array}{c}=\frac{4}{30}\\ =0.1333\\ =13.33\%\end{array}$