Question

Approximate ?(68.5 < ?̅ < 71.5) when ?̅ is the mean of a random sample of size 12 from a distribution with ? = 70 and variance of 75.

Answer 1

Solution :

Given that ,

mean = = 70

variance=75

standard deviation = = 75=8.6603

standard deviation = =8.6603

n = 12

= 70

=  / n= 12 / 8.6603=4.0778

P(68.5<    <71.5 ) = P[(68.5 - 70) / 4.0778< ( - ) / < (71.5 - 70) / 4.0778)]

= P(-0.37 < Z < 0.37)

= P(Z <0.37 ) - P(Z <-0.37 )

Using z table

=0.6443 -0.3557

=0.2886

probability= 0.2886