Statistics Problem

Question

What is the probability a random sample of size 15 will have a mean gestation period within 10 days of the mean?

Mean= 183

Standard Deviation = 16

Answer 1

Prob ( 173 < mean < 193) =

Prob ( mean < 193) - Prob ( mean < 173)

Zmin = (173 - 183)/ (16/sqrt(15))

= -10* sqrt(15)/16

= -(5/8) * sqrt(15)

= -2.4206

Zmax = (193 - 183)/ (16 / sqrt(15))

= (5/8) sqrt(15)

= 2.4206

Prob ( zMin < zMean < zMax) =

Prob( z < 2.4206) - Prob(z < -2.4206) =

-

98.4505%