The incomes in a certain large population of college teachers have a normal distribution with mean $75,000 and standard deviation $10,000. Four teachers are selected at random from this population to serve on a salary review committee. The probability that their average salary is less than $65,000 is closest to .

The probability that their average salary is less than $65,000 is closest to 2.28%.

Step-by-step explanation:

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

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore 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 pvalue, 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 random variable X, with mean and standard deviation , a large sample size can be approximated to a normal distribution with mean and standard deviation, which is also called standard error

In this problem, we have that:

The probability that their average salary is less than $65,000 is closest to

This is the pvalue of Z when X = 65000. So

By the Central Limit Theorem

has a pvalue of 0.0228.

The probability that their average salary is less than $65,000 is closest to 2.28%.

the highest percentage for deaths in construction from highest to lowest is as follows: falls, struck by objects, electrocution, and caught-in/between. these four are collectively known as fatal four.

in the case of falls, the type that is responsible for the overall highest death in the category is falls from roofs.

step-by-step explanation:

graph using a few selected

x         y

-1       15

0         6

1         2.4

2       0.96