Answer to Question #187331 in Statistics and Probability for Khalilah Spencer

Question

The annual dollar value of homes sold by real estate salespersons in a certain

community has a mean of $7.5 million, with a standard deviation of $4.4 million.

Find the probability that, in a random sample of 36 such salespersons, the sample

mean annual dollar value of homes sold will

(i) be less than $6.5 million; [2 marks]

(ii) exceed $9.0 million.

Answer 1

$\mu = 7.5 \\ \sigma = 4.4 \\ n = 36$

(i)

$P(X<6.5) = P(Z < \frac{6.5 -7.5}{4.4/ \sqrt{36}}) \\ = P(Z< -1.393) \\ = 0.0818$

(ii)

$P(X>9.0) = 1 -P(X<9.0) \\ = 1 -P(Z < \frac{9.0 -7.5}{4.4 / \sqrt{n}} ) \\ = 1 -P(Z < 2.045) \\ = 1 -0.9795 \\ = 0.0205$