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The labour charge for repairs at an automobile service center are
based on a standard time specified for each type of repair. The time
specified for replacement of universal joint in a drive shaft is one
hour. The manager reviews a sample of 30 such repairs. The average
of the actual repair times is 0.86 hour with standard deviation 0.32
hour.
a. Test at the 1% level of significance the null hypothesis that the
actual mean time for this repair differs from one hour.
b. The sample mean is less than one hour, suggesting that the mean
actual time for this repair is less than one hour. Perform this test, also
at the 1% level of significance. (The computation of the test statistic
done in part (a) still applies here.)
A magazine publisher tells potential advertisers that the mean household income of its regular readership is $61,500. An advertising agency wishes to test this claim against the alternative that the mean is smaller. A sample of 40 randomly selected regular readers yields mean income $59,800 with standard deviation $5,850. Perform the relevant test at the 1% level of significance.

Two questions A and B were given to 50 students as class work. 23 of them could answer question A but not B. 15 of them could answer B but not A. If 2x of them could answer none of the two questions and 2 could answer both questions.

Represent the information in a Venn diagram. (b) Find the value of x


A new pub has opened in town and you’re considering it as a potential new spot for cheap
wings and beer. Before going, you chat with a group of 12 friends who have already been. You
obtain the following information:
Three of them complained about the quality of the beer.
Four of them complained about the quality of the wings.
Two of them complained about the quality of the beer and wings.
Three of them had no complaints.
Answer the following questions:
a. What is the probability you will enjoy the beer?
b. What is the probability you will enjoy the wings?
c. What is the probability you will dislike either the wings, or the beer, or both?
d. What is the probability you will enjoy both the beer and the wings?
e. Why have twelve of your friends already been here, but none have invited you
3)A population consists of four numbers 3, 7, 11, 15. Consider all possible samples of size two which can
be drawn (a) with replacement (b) without replacement from this population. Find i) The mean of the
population ii) The standard deviation of the population iii) The mean of the sampling distribution of means
iv) The standard deviation of the sampling distribution of means.
What is the SAMPLE STANDARD DEVIATION (use your calculator) of this data set?

4, 6, 11, 6, 8, 7

(Round to the 2nd decimal place: Example 7.32

1. A new pub has opened in town and you’re considering it as a potential new spot for cheap wings and beer. Before going, you chat with a group of 12 friends who have already been. You obtain the following information:

Three of them complained about the quality of the beer.

Four of them complained about the quality of the wings.

Two of them complained about the quality of the beer and wings.

Three of them had no complaints.

Answer the following questions:

a. What is the probability you will enjoy the beer?

b. What is the probability you will enjoy the wings?

c. What is the probability you will dislike either the wings, or the beer, or both?

d. What is the probability you will enjoy both the beer and the wings?


How to find the probability when given the mean and standard deviation
From a group of 10 men and 15 women, how many committees of size 9 are possible a) with no restrictions; b) with 6 men and 3 women; c) with 5 men and 4 women if a certain man must be on the committee?
In a departmental examination on statistics, the mean grade was 64 and the standard deviation was 10. If the grades are approximately normally distributed and 40 students got grades between 60 and 70, how many students took the examination?
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