Exercises. 1. Using the table for the distribution, find

1. Using the table for the distribution, find

a) The upper 5 % point when n = 9

b) The upper 1 % point when n =18

c) The lower 2.5 % point when n =12

d) The lower 1 % point when n =24.

2. Find the probability of

a)

b)

c) , when n =11

d) , when n =9

3. The monthly salaries of part time working students follow a normal distribution with standard deviation of 3 000 tg. A random sample of 24 observations was taken.

a) Find the probability that sample standard deviation is more than 4 000 tg.

b) What is the probability that sample standard deviation is less than

2 000 tg?

4. A random sample of 10 households was taken. Suppose that the electric bill they pay follow a normal distribution.

a) The probability is 0.1 that sample variance is greater than what percentage of the population variance?

b) Find any pair of numbers, a and b, such that the following statement holds: The probability is 0.90 that the sample variance is between a %

and b % of the population variance.

5. A production process follows a normal distribution. A sample of 15 produced items was selected.

a) The probability is 0.95 that the sample variance is more than what percentage of the population variance?

b) The probability is 0.99 that the sample variance is greater than what percentage of the population variance?

c) Find any pair of numbers, a and b, such that the following statement holds: The probability is 0.95 that the sample variance is between a %

and b % of the population variance.

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