Question

A study finds that eight year old American children spend an average of 4.9 hours watching TV or playing video games on Sundays with a standard deviation of 2.08 hours. Find the probability that a randomly selected American eight year old would spend between 5 and 6 hours watching television or playing video games on a Sunday.
Assume the distribution is normal. Draw the distribution and shade the region in question. Then find the area of the shaded region.

Answer 1

Solution :

Given that ,

mean =   = 4.9

standard deviation = = 2.08   

n = 8

= 4.9

=  / n= 2.08 / 8=0.7354

P(5<     <6 ) = P[(5-4.9) /0.7354  < ( - ) /   < (6-4.9) /0.7354 )]

= P( 0.14< Z < 1.50)

= P(Z < 1.50) - P(Z <0.14 )

Using z table

=0.9332-0.5557

=0.3775

probability= 0.3775