Question

Suppose a random sample of n = 25 observations is selected from a population that is normally distributed with mean equal to 109 and standard deviation equal to 15.

(a) Find the probability that x exceeds 113.

(b) Find the probability that the sample mean deviates from the population mean μ = 109 by no more than 5.

Answer 1

Given n=25 u=log TECS.D)- 15 G a) probability that exccede 113 PCX > 113) PEX-u > 013-1 13-109) P (274) P( 23 0.26) from standood 1-p(220.26) = 1-060.26) normal table 1-0.60 26 LP (7 3113) = 0.3974 b) Sample mean (7) deviates from pop" mean (el) = 10g by no more than 5 P (X-155) PCX 25tu) we know that all N N00, 1) ohn P ( X - U 215+10g) - 4) ohn f (x-2 < 1 4 - 9 own 15 / 25 przes) from standard normal P (2 2 1.66) table 0 (1.66) = 0.9515 - [p (X=425) = 0.9515