Question

A random variable follows a normal distribution with a mean of 825 and std. dev. of 224. What is the probability of gathering a sample of 25 observations and the sample average falls below 725 or above 925?

Answer 1

Given ,

= 825 , = 224

Using central limit theorem,

P( < x) = P (Z < x - / / sqrt(n) )

So,

P( 725 < < 925) = P( <925) - P( < 725)

= P( Z < 925 - 825 / 224 / sqrt(25) ) - P( Z < 725 - 825 / 224 / sqrt(25) )

= P( Z < 2.2321) - P( Z < -2.2321)

= 0.9872 - 0.0128

= 0.9744

Therefore,

P( < 725 or > 925) = 1 - P( 725 < < 925)

= 1 - 0.9744

= 0.0256