Answer to Question #152419 in Statistics and Probability for Shawnitra Jackson

Question

According to a recent survey, the salaries of assistive professors have a mean of $41,750 and a standard deviation of $7500. Assuming that the salaries of assistive assessors follow a normal distribution, find the proportion of assistance professors who are at most $48,000. Where are you answer to at least four decimal places.

Answer 1

μ = 41750

x = 48000

σ = 7500

$P(x≤48000) = P(Z \leq \frac{x-μ}{σ}) \\ = P(Z \leq \frac{41750-48000}{7500}) \\ =P(Z \leq \frac{-6250}{7500}) \\ = P(Z\leq-0.8333) \\ = 0.2024$