A sample of size 65 will be drawn from a population with mean 22 and standard deviation 15. Find the probability that will be between 21 and 25.

Answer 1

P(21 < xbar < 25)

transform limit of inequality to z:

(xbar - mu)/(sd/sqrt(n))

= P( (21-22)/(15/sqrt(65) < z < (25 - 22)/(15/sqrt(65))

= P( -0.54 < z < 1.612)

= P(z < 1.612) - P(z < -0.54)