Question

A normally distributed population has a mean of 71 and a standard deviation of 15. Determine the probability that a random sample of size 37 has an average between 74 and 78.

Round to four decimal places.

Answer 1

Solution :

Given that,

mean = = 71

standard deviation = =15

n=37

= 71

=  / n = 15 / 37=2.4660

= P(74<    <78 ) = P[(74 - 71) / 2.4660< ( - ) / < (78 - 71) / 2.4660)]

= P( 1.22< Z <2.84 )

= P(Z <2.84 ) - P(Z < 1.22)

Using z table,  

= 0.9977 - 0.8888

= 0.1089