1. A random sample of size n = 40 is selected from a binomial distribution with population proportion p = 0.25.

(a) What will be the approximate shape of the sampling distribution of p?skewed to the leftskewed to the right normal

(b) What will be the mean and standard deviation (or standard error) of the sampling distribution of p? (Round your answers to four decimal places.)

mean
standard deviation

(c) Find the probability that the sample proportion p is between 0.11 and 0.48. (Round your answer to four decimal places.)

2. A random sample of size n = 36 is selected from a population with mean = 56 and standard deviation = 30.

(a)What will be the approximate shape of the sampling distribution of x?

normal skewed symmetric

(b)What will be the mean and standard deviation of the sampling distribution of x? mean standard deviation

3. (a) Give the mean and the standard deviation of the sampling distribution of the sample mean x.

mean
standard deviation

(b) Find the probability that x exceeds 113. (Round your answer to four decimal places.) (c) Find the probability that the sample mean deviates from the population mean = 104 by no more than 3. (Round your answer to four decimal places.) You may need to use the appropriate appendix table to answer this question.

4. Calculate SE(p) for n = 100 and these values of p. (Round your answers to four decimal places.)

(a)p = 0.01SE(p) =

(b)p = 0.20SE(p) =

(c)p = 0.30SE(p) =

(d)p = 0.50SE(p) =

(e)p = 0.70SE(p) =

(f)p = 0.80SE(p) =

(g)p = 0.99SE(p) =

(h)Plot SE(p) versus p on graph paper and sketch a smooth curve through the points. For what value of p is the standard deviation of the sampling distribution of p a maximum?

g). What happens to the standard error when p is near 0 or near 1.0? choose answer from below.

The standard error is large near 0 and small near 1.0.

The standard error is small near 0 and large near 1.0.

The standard error is small near 0 and 1.0.

The standard error is equal for all values of p.

The standard error is large near 0 and 1.0.