A population of values has a normal distribution with mean = 49.1 and standard deviation = 8.9. You intend to draw a random sample size of n = 165. Determine the mean and the standard deviation of the sampling distribution x

What is the mean of the sampling distribution of x

Mean x =

What is the standard deviation of the sampling distribution of x

Standard deviation x = ----

2- According to the American Time Use Survey, Americans sleep an average of 8.45 hours each day with a standard deviation of 2.45 hours. Let sampling distribution x be the average of a random sample of Americans. What sample size will give the standard deviation of sampling distribution x equal to 0.41 hours?

Round solution up to the nearest number, if necessary.

n =

3- Suppose a left-skewed distribution exists with a mean of 142 and standard deviation of 19. Consider a random sample of 31 observations. Use this information to determine the following probabilities. Round solutions to four decimal places, if necessary.

Find the probability that a random sample of size 31 has a mean less than 139

P(sampling distribution x < 139) =

Find the probability that a random sample of size 31 has a mean between 131 and 138.

P(131 < samplingdistribution x < 138) =

3- According to the American Time Use Survey, American age 15 and over spend an average of 2.57 hours each day watching TV. The distribution of all such amounts of time spent watching TV is normally distributed with a standard deviation of 1.09 hours. Use this information to determine the following two probabilities. Round solutions to four decimal places, if necessary.

Find the probability that a single randomly American watches TV less than 2,54 hour per day.

P(x < 2.54) = --

Find the probability that the mean time spend watching TV per day of a random sample of 76 Americans is less than 2.54 hours.

P(sampling distribution x < 2.54) =