Statistics and Probability Answers

2) For a certain type of fluorescent light in a large building, the cost per bulb of replacing bulbs all at once is much less than if they are replaced individually as they burn out. It is known that the lifetime of these bulbs is normally distributed, and that 60% last longer than 2500 hours, while 30% last longer than 3000 hours.

a) What are the approximate mean and standard deviation of the lifetimes of the bulbs?

b) If the light bulbs are completely replaced when more than 20% have burned out, what is the time between complete replacements?

We want to know if 2 different professors are teaching two different section of the same

statistics course differently. The following are the test scores for the 15 students from

section (A) and 15 students from section (B).

Section (A) 81 83 72 74 79 95 62 90 86 72 67 79 93 80 75

Section (B) 79 82 75 82 81 97 64 88 80 74 63 79 94 85 68

Use the sign test at 0.05 level of significance

The nutritionist and medical doctors have always believed that Vitamin C is highly

effective in reducing the incidents of colds. To test this belief, a random sample of 13

persons is selected and they are given daily doses of Vitamin C under medical supervision

over a one-year period. The number of codes each person catches during the year is

recorded and a comparison is made with the number of colds contracted by each such

person during the previous year. This comparison is tabulated as follows, along with the

sign of the change.

Observation 1 2 3 4 5 6 7 8 9 10 11 12 13

Without

Vitamin C

7 5 2 3 8 2 4 4 3 7 6 2 10

With

Vitamin C

2 1 0 1 3 2 3 5 1 4 4 3 4

Use the sign test at 0.05 level of significance, determine if Vitamin C is effective in reducing

colds.

The personnel director of a company wishes to select applicants for advanced training

without regard to sex. Let ‘W’ denote women and ‘M’ denote men and the pattern of arrival

be ‘M WWW MMM WW M WWWW MMMM W M W MM WWW MM W MMMM

WW M WW MMMM WW M WWWW MM WW M W M WW’. Will you conclude that

the applicants have arrived in a random fashion?

29) The following arrangement shows the rise(U) or fall(D) in the price of an equity share on

40 consecutive trading days on which its price did not remain the same:

U U D D U U U D U U U D D U D D D U D D U D D U U U U D D D D U U D U U D D D

U

Test the hypothesis that this arrangement of Us and Ds is random at α =0.05 level of

significance.

30) The sequence of occurrence of ‘zeros’ and ‘ones’ in a message sent in a digital code is

shown below. Test at 5 percent whether the sequence of ‘0’ and ‘1’ is random 00110 11011

00001 11100 00110 11001 11110 00011 00100 11000 11100 00011 11100 00000 11111

10001 11000 10001 01110.

Vanaspati oil is marketed in tins of 10 kg. A sample of 20 tins showed the mean weight as

9.5kg with standard deviation of 3 kg. Does the sample justify the claim that the mean

weight is 10 kg. Mention the level of significance, you use.

24) A random sample of 16 observations has mean 103.75cm. The sum of the squares of the

deviations from the mean is 843.75 cm. Can this sample be regarded as coming from the

population having 108.75cm as the mean?

25) A company supplies tooth-paste in a packing of 100gm. A sample of 10 packing’s gave the

following weights in gm.

100.5, 100.3, 100.1, 99.8, 99.7, 99.7, 100.3, 100.4, 99.2, 99.3

Does the sample support the claim of the company that the packing weighs 100 gm?