**Answer:**

0.16 probability that in a sample of 25 mosquitoes the mean body temperature is greater than 59∘F, assuming the underlying distribution is normal.

**Step-by-step explanation:**

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

**Normal Probability Distribution:**

Problems of normal distributions can be solved using the z-score formula.

In a set with mean and standard deviation , the z-score of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

**Central Limit Theorem**

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

**The body temperatures of all mosquitoes in a county have a mean of 57∘F and a standard deviation of 10∘F.**

This means that

**Sample of 25:**

This means that

**of 25 mosquitoes the mean body temperature is greater than 59∘F, assuming the underlying distribution is normal?**

This is 1 subtracted by the pvalue of Z when X = 59. So

By the Central Limit Theorem

has a pvalue of 0.84

1 - 0.84 = 0.16

0.16 probability that in a sample of 25 mosquitoes the mean body temperature is greater than 59∘F, assuming the underlying distribution is normal.