You are in charge of decorating your gym for a home coming dance. You bought 6 bags of balloons and 5 bags of sparkling balloons
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population mean, μ =135
population standard deviation, σ = 15
sample size, n = 19
Assume a large population, say > 100,
we can reasonably assume a normal distribution, and a relatively small sample.
The use of the generally simpler formula is justified.
Estimate of sample mean
Estimate of sample standard deviation
Thus, using the normal probability table,
Therefore
The probability that the mean weight is between 125 and 130 lbs
P(125<X<130)=0.0731166-0.0018308
=0.0712858