SOLUTION: 4. The amount of ice cream in a cone has a distribution with a mean of 3.2 ounces per cone and a standard deviation of 0.4 ounces. If there are 50 children to be served ice cream

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Question 364527: 4. The amount of ice cream in a cone has a distribution with a mean of 3.2 ounces per cone and a standard deviation of 0.4 ounces. If there are 50 children to be served ice cream at a birthday party, find the probability that more than 165 ounces of ice cream will be served.
Found 2 solutions by stanbon, jrfrunner:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
The amount of ice cream in a cone has a distribution with a mean of 3.2 ounces per cone and a standard deviation of 0.4 ounces. If there are 50 children to be served ice cream at a birthday party, find the probability that more than 165 ounces of ice cream will be served.
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165/50 = 3.3
t(3.3) = (3.3-3.2)/0.4 = 0.25
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P(x > 3.3) = P(t> 0.25) = 0.4018
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Cheers,
Stan H.

Answer by jrfrunner(365) (Show Source):
You can put this solution on YOUR website!
you give the following
a distribution with and
also you sample 50 children n=50 then you asked
find the probability that more than 165 ounces of ice cream will be served
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We have no idea what kind of distribution these data come from.
But saying P(total amount of ice cream>165)=P(Xbar>165/50)=P(xbar>3.3)
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We dont know the distribution, but since the analysis is based on the distribution of "averages" and the sample size is large (ie >30) we can rely on the Central Limit theorem to enables us to use the Normal distribution.
P(Xbar>3.3)=P(Z>1.77)=0.038 where Z=(Xbar-)/(/sqrt(n))