Question

The times that college students spend studying per week have a distribution skewed to the right with a mean of 7.6 hours and a standard deviation of 2.6 hours. Find the probability that the mean time spent studying per week for a random sample of 45 college students would be

a. between 7.0 and 7.9 hours.

Round your answer to two decimal places.

P=____

b. less than 7.3 hours.

Round your answer to two decimal places.

P=____

Answer 1

Given that ,

mean = = 7.6

standard deviation = =2.6

n = 45

= 7.6

=  / n= 2.6 / 45=0.3876

P(7.0 <     <7.9 ) = P[(7.0 -7.6) / 0.3876< ( - ) / < (7.9 -7.6) /0.3876 )]

= P( -1.55< Z <0.77 )

= P(Z <0.77 ) - P(Z < -1.55)

Using z table

=0.7794-0.0606

=0.7188

probability= 0.72

(b)

P( <7.3 ) = P[( - ) / < (7.3 -7.6) /0.3876 ]

= P(z <-0.77 )

Using z table  

= 0.2206

probability=0.22