Question

1. Suppose the selling price of homes in the United States is skewed right with a mean of $350,000 and a standard deviation of $160,000.

1. (4 pts) If we record the selling price of 40 randomly selected U.S. homes, what will be the shape of the distribution of sample means? What will be the mean of this distribution? What will be the standard deviation of this distribution? Indicate how you arrived at your conclusions.

2. (6 pts) What is the probability that in a random sample of 40 U.S. homes, the mean selling price is greater than $400,000?

Answer 1

a)This is a normal distribution question with

\\Mean (\mu)= 350000 \\Standard\;Deviation (\sigma)= 160000 Sample size (n) = 40

Shape of the distribution of sample means is symmetric

Since we know that

b)

P(x > 400000.0)=?

The z-score at x = 400000.0 is,

z = 1.9764

This implies that

P(x > 400000.0) = P(z > 1.9764) = 1 - 0.9759452542188739

PS: you have to refer z score table to find the final probabilities.

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