Statistics and Probability Answers

The average travel time to work for a person living and working in​ Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time is approximately normally distributed.

Which of these statements is asking for a measurement​ (i.e. is an inverse normal​ question)?

A.

What percentage of people living and working in Kokomo have a travel time to work that is between thirteen and fifteen​minutes?

B.

If​ 15% of people living and working in Kokomo have travel time to work that is below a certain number of​ minutes, how many minutes would that​ be?

Use the empirical rule to solve the problem.

At one​ college, GPA's are normally distributed with a mean of 2.9 and a standard deviation of 0.5. What percentage of students at the college have a GPA between 2.4 and 3.4​? Round to the nearest percent.

A.

Almost all

B.

​68%

C.

​84%

D.

​95%

 A random sample of 12 financial analysts was asked to predict the percentage increases in the prices of two common stocks over the next year. The data are: 

Analyst: A, B, C, D, E, F, G, H, I, J

Stock 1: 6.8, 9.8, 2.1, 6.2, 7.1, 6.5, 9.3, 1.0, -0.2,9.6

Stock 2: 6.2, 12.3, 5.3, 6.8, 7.0, 6.2, 10.1, 2.7, 1.3, 9.8 

Use the sign test and Wilcoxon sign rank test to test the null hypothesis that, for the population of analysts there is no overall preference for increases in one stock over the other.

 A plastic Manufacturer tests the tensile strength of different type of polythene material. A sample of three measurements is taken for each material type and data in pounds per square inch are as follows: 

Type-I: 200 215 218 220

Type-II: 260 255 277 250

Type-III:245 240 270 -

Determine, if the mean tensile strength of the three different types of materials differ significantly. 

10 children, each one selected from 10 sets of identical twins was trained by a certain method A and the remaining 10 children were trained by method B. At the end of the year, following 1.Q score were obtained: 

Pair : 1 2 3 4 5 6 7 8 9 10

Method A: 124 118 127 120 135 .130 140 128 140 126

Method B:131 127 135 128 137 131 132 125 141 118 

Is this sufficient evidence to indicate a difference in the avenge 1.Q score of the two groups?

To compare the price of a certain product in two cities, ten shops were selected random in each city. The following observations were obtained: 

City A: 61 63 56 63 56 62 59 60 61 65

City B: 55 54 47 59 51 61 57 54 64 58 

Test whether the average price can be said to be the same in the two cities (5% level of significance). 

Patients of a clinic are tested for a particular desease. For each patient, the result of the test – ‘infected’/’not infected’ – is correct with the probability 0.8. Suppose that 20% of the patients are infected. What is the probability that a given patient is indeed infected if his/her test result shows ‘infected’?

 ◦ 0.4 ◦ 0.5 ◦ 0.6 ◦ 0.64 ◦ 0.8

I suppose the answer is 0.8 since that is the probability that a result is accurate.

A manufacturer of fluorescent tubes claims that average life rime is more than 1750 hour, A sample of 400 fluorescent light bulbs produced mean life tone 1600 hours with a standard deviation of ISO hours. Does the claim of the company justified at 5% level of significance?