Question

Please, help me on this question, guys! I know the answer for (a) so I'll write down, too. For (b) I tried "$89,000 because that is the price with the biggest unusual z-score" but I got that this part is incorrect because I needed to use the mean and standard deviation that I calculated along with z=2 to determine the threshold higher price. That got me lost.
Question: Consider the following prices for a sample of 10 Congo-imported black diamonds: $34,550; $45,500; $75,000; $33,000; $89,000; $40,000; $55,000, $62,500; $88,000; $81,750.

(a) Calculate mean and standard deviation for the above list of prices. Answer: Mean is 60,430 and Std Dev is 21,958.0813.

(b) What is the higher price you will pay for a Congo-imported diamond based on the sample from above? Explain your rationale for that.

Answer 1

Let x be a random variable representing the price of a Congo-imported black diamond. Let the higher price be p. Then,
P(x < p) = P(x < (p - mean)/sd) = P(x < (p - 60,430)/21,958.08) = P(z < 2)
Therefore,
(p - 60,430)/21,958.08 = 2
p - 60,430 = 2 x 21,958.08 = 43,916.16
p = 34,916.16 + 60,430 = 104.346.16

Therefore, The required price is $104,346.16