The mean amount of ice cream consumed by the college student

The mean amount of ice cream consumed by the college students annually can be approximately normally distributed at 17.9 pounds with a standard deviation of 4.4 pounds. If you randomly select a group of 30 college students, what is the probability that the mean amount of ice cream in the group is between 13 and 16 pounds?

Solution

z = (x - m) / (sd / sqrt(n) )

Mean m = 17.9

SD = 4.4

n = 30

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P(13 < x < 16) = P( (13 - 17.9)/(4.4/sqrt(30)) < z < (16-17.9)/(4.4/sqrt(30)) )

= P(-6.10 < z < -2.37)

= P(z < -2.37) - P(z < -6.10)

= 0.0089 - 0

= 0.0089