A random sample of size 31 is to be chosen from population that has a mean ? = 53 and standard deviation ? of 13.
(a) This sample of 31 has mean value of x, which belongs to a sampling distribution. Determine the shape of this sampling distribution.
Skewed right approximately normal skewed left chi-square
(b) Determine the mean of this sampling distribution. (Give your answer correct to nearest whole number.)
(c) Determine the standard error of this sampling distribution. (Give your answer correct to two decimal places.)
(d) What is the probability that this sample mean will be between 40 and 55? (Give your answer correct to four decimal places.)
(e) What is the probability that the sample mean will have a value greater than 52? (Give your answer correct to four decimal places.)
(f) What is the probability that the sample mean will be within 2 units of the mean? (Give your answer correct to four decimal places.)