Question

1) The mean lifetime of a tire is 36 months with a variance of 49. If 126 tires are sampled, what is the probability that the mean of the sample would differ from the population mean by greater than 0.44 months? Round your answer to four decimal places.

2) Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.5 years with a standard deviation of 1.1 years.

a) If a sampling distribution is created using samples of the ages at which 47 children begin reading, what would be the mean of the sampling distribution of sample means? Round to two decimal places, if necessary.

b) If a sampling distribution is created using samples of the ages at which 47 children begin reading, what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary.

3) A production manager at a wall clock company wants to test their new wall clocks. The designer claims they have a mean life of 15 years with a variance of 25. If the claim is true, in a sample of 41 wall clocks, what is the probability that the mean clock life would be less than 15.4 years? Round your answer to four decimal places.

Answer 1

1) Let denotes the sample mean of 126 tires, Then follows a Normal distribution with mean 36 and standard deviation:

. thus the probability that the mean of the sample would differ from the population mean by greater than 0.44 months is given by:

.

Thus the answer is 0.031

2) (a). The mean of the sampling distribution of sample means will be 5.5 years.

(b). The standard deviation of the sampling distribution of sample means is given by:

3)

Let denotes the sample mean life of 41 clocks, Then follows a Normal distribution with mean 15 and standard deviation:

. Thus the probability that the mean clock life would be less than 15.4 years is given by:

Thus the answer is 0.6958