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A survey of high school students revealed that the number of soft drinks consumed per month...

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

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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

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