During the summer months, the prices of nonsmoking rooms with a king-sized bed in hotels in a certain area are roughly normally distributed with a mean of $131.80 and a standard deviation of $29.12. a travel agent randomly selects prices of nonsmoking rooms with a king-sized bed from 15 hotels in the area. what is the probability that their average cost will be more than $150

Question

Katie

Mathematics

5 June, 06:17

During the summer months, the prices of nonsmoking rooms with a king-sized bed in hotels in a certain area are roughly normally distributed with a mean of $131.80 and a standard deviation of $29.12. a travel agent randomly selects prices of nonsmoking rooms with a king-sized bed from 15 hotels in the area. what is the probability that their average cost will be more than $150

+3

Answers (1)

Know the Answer?

Nathalia Powers · Answer 1

Population mean (u) = $131.80 Standard deviation (sd) = $29.12 Sample number (n) = 15 Sample mean = $150 Using Z score formula ... Z = (150 - 131.80) / (29.12) / 15^1/2 Z = 2.420 Area under the curve (alpha) with Z = 2.420 = 49.22 In percentage Alpha = 0.4922 Probability = 1-Alpha Probability = 1 - 0.4922 = 0.5078