Question

Time spent using​ e-mail per session is normally​ distributed, with mu equals 7 minutes and sigma equals 2 minutes. Assume that the time spent per session is normally distributed. Complete parts​ (a) through​ (d). a. If you select a random sample of 25 ​sessions, what is the probability that the sample mean is between 6.8 and 7.2 ​minutes?

Answer 1

Solution :

Given that,

mean = = 7

standard deviation = = 2

n=25

= 7

=  / n = 2/ 25=0.4

= P(6.8<    <7.2 ) = P[(6.8 - 7) /0.4 < ( - ) / < (7.2 - 7) /0.4 )]

= P( -0.5< Z <0.5 )

= P(Z <0.5 ) - P(Z <-0.5 )

Using z table,  

=0.6915 -0.3085   

= 0.3830