Answer to Question #232365 in Statistics and Probability for awd

Question

The result of a survey shows that the amount of time a student spends on studying for a test is normally distributed. If the amount of time spent studying is 12 hours and the standard deviation is 4 hours, what is the probability that a student will spend more than 8 hours studying?

Answer 1

$\mu=12 \\ \sigma=4 \\ P(X>8) = 1 -P(X≤8) \\ = 1 -P(Z≤ \frac{8-12}{4}) \\ = 1 -P(Z≤ -1) \\ = 1 -0.1586 \\ = 0.8414$