Question

Random sample of size 25 from a normally distributed population with the mean of 4 and variance of 16. Find the point estimate of the population mean if P(X>x)=0.9798.

Answer 1

$n=25 \\ \mu=4 \\ \sigma^2 = 16 \\ \sigma=4 \\ P(X>x) = 0.9798 \\ P(X≤x) = 1 -0.9798 = 0.0202 \\ P(Z≤ \frac{x- 4 }{4 / \sqrt{25}}) = 0.0202 \\ \frac{x- 4 }{4 / 5} = -2.049 \\ x -4= -1.64 \\ x = 4-1.64=2.36$