Answer to Question #166372 in Statistics and Probability for Denden

Question

The average daily jail population in the New Bilibid prison in Muntinlupa City is 36,295. If the distribution is normal and the standard deviation is 3,760, find the probability that on a randomly selected day, the jail population is greater than 40,145.

Answer 1

$μ = 36295 \\ σ = 3760 \\ P(X>40145) = P(\frac{x-μ}{σ} > \frac{40145-36295}{3760}) \\ = P(Z > 1.024) \\ = 1 -P(Z<1.024) \\ = 1 -0.8470 \\ = 0.153$