Question

X is a random variable for the weight of a steak. The distribution of X is assumed to be right skewed with a mean of 3.5 pounds and a standard deviation of 2.32 pounds.

1. Why is this assumption of right skewed reasonable?

2. Why cant you find the probability that a randomly chosen steak weighs over 3 pounds?

3. 5 steaks randomly selected, can u determine the probability that the average weight is over 3 pounds? Explain.

4. 12 people pick steaks, each pick 5, total of 60 steaks chosen: A) what is the sampling distribution for the mean of this sample, include mean and standard deviation of the distribution.

B) If the mean weight of 60 steaks was less than 2.5 pounds would u be shocked, justify with calculations.

Answer 1

1:

Yes because only some steak will have very high weight. Most of the steaks will be have almost equl weight.

2:

Since distribution of the weight of a steak assumed to be right skewed and sample size is less than 30 so we cannot apply CLT.

3:

No, because sample size is less than 30 so we cannot apply CLT.

4:

A)

The sampling distribution sample mean will be approximately normal with mean

and standard deviation is

B)

The z-score for is

The required probability is: