Question

A survey of high school students revealed that the number of soft drinks consumed per month was normally distributed with a mean of 25 and standard deviation 15. A sample of 36 students was selected. What is the probability that the average number of soft drinks consumed per month for the sample was between 28.7 and 30 soft drinks

Answer 1

Given

= 25 , = 15

Using central limit theorem,

P( < x) = P(Z < ( x - ) / ( / sqrt(n) ) )

So,

P(28.7 < < 30) = P( < 30) - P( < 28.7)

= P(Z < ( 30 - 25) / ( 15 / sqrt(36)) ) - P(Z < ( 28.7 - 25) / ( 15 / sqrt(36)) )

= P(Z < 2) - P(Z < 1.48)

= 0.9772 - 0.9306 ( from Z table)

= 0.0466