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1.Determine whether each of the...

1.Determine whether each of the distributions given below represents a probability distribution. Justify your answer.

(A)

x 1 2 3 4

P(x) 1/4 1/12 1/3 1/6

(B)

x 3 6 8

P(x) 0.2 2/5 0.3

(C)

x 20 35 40 50

P(x) 0.3 -0.1 0.5 0.3

2.Answer the following:

(A) Find the binomial probability P(x = 5), where n = 13 and p = 0.50.

(B) Set up, without solving, the binomial probability P(x is at most 5) using probability notation.

(C) How would you find the normal approximation to the binomial probability P(x = 5) in part A? Please show how you would calculate µ and s in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations

3.A sample of 134 golfers showed that their average score on a particular golf course was 93.23 with a standard deviation of 6.25.

Answer each of the following (show all work

and state the final answer to at least two decimal places.):

(A) Find the 98% confidence interval of the mean score for all 134 golfers.

(B) Find the 98% confidence interval of the mean score for all golfers if this is a sample of 110 golfers instead of a sample of 134.

(C) Which confidence interval is larger and why

4.Assume that the population of heights of female college students is approximately normally distributed with mean ? of 64.64 inches and standard deviation ? of 6.02 inches. A random sample of 98 heights is obtained. Show all work.

(A) Find P(x>63.75)

(B) Find the mean and standard error of the x distribution

(C) Find P(x> 63.75)

(D) Why is the formula required to solve (A) different than (C)?

(A)

x 1 2 3 4

P(x) 1/4 1/12 1/3 1/6

(B)

x 3 6 8

P(x) 0.2 2/5 0.3

(C)

x 20 35 40 50

P(x) 0.3 -0.1 0.5 0.3

2.Answer the following:

(A) Find the binomial probability P(x = 5), where n = 13 and p = 0.50.

(B) Set up, without solving, the binomial probability P(x is at most 5) using probability notation.

(C) How would you find the normal approximation to the binomial probability P(x = 5) in part A? Please show how you would calculate µ and s in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations

3.A sample of 134 golfers showed that their average score on a particular golf course was 93.23 with a standard deviation of 6.25.

Answer each of the following (show all work

and state the final answer to at least two decimal places.):

(A) Find the 98% confidence interval of the mean score for all 134 golfers.

(B) Find the 98% confidence interval of the mean score for all golfers if this is a sample of 110 golfers instead of a sample of 134.

(C) Which confidence interval is larger and why

4.Assume that the population of heights of female college students is approximately normally distributed with mean ? of 64.64 inches and standard deviation ? of 6.02 inches. A random sample of 98 heights is obtained. Show all work.

(A) Find P(x>63.75)

(B) Find the mean and standard error of the x distribution

(C) Find P(x> 63.75)

(D) Why is the formula required to solve (A) different than (C)?

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