Question

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean equals 137 days and standard deviation equals 12 days. The probability that a random sample of size 17 will have a mean gestation period within 12 days of the mean is ?

.

Answer 1

Solution :

Given that,

mean = = 137 days

standard deviation = = 12 days

n = 17

= 137 days

= / n = 12 / 17 = 2.91

137 ± 12 = 125,149

P(125 < < 149)  

= P[(125 - 137) / 2.91 < ( - ) / < (149 - 137) / 2.91)]

= P( -4.12 < Z < 4.12)

= P(Z < 4.12) - P(Z < -4.12)

Using z table,  

= 1 - 0  

= 1