13 Use the central limit theorem to find the probability tha

13. Use the central limit theorem to find the probability that the average number of moths in 40 traps is greater than 0.6. Use CrunchIt! and give your answer to four decimal places.

Solution

?=0.5, ?=0.6, n=40

According to the central limit theorem, the mean value of a sample with a large enough sample size is normally distributed.
If a sample of size n is drawn from a population with mean ? and standard deviation ?, then the sample mean Xbar is normally distributed with mean ? and standard deviation ?/?n.

Any normally distributed variable X with mean ? and standard deviation ?,
X ~ N( ? , ?