Question

In a rural town, the average high school teacher annual salary is $43,000. Let the salary be normally distributed with a standard deviation of $18,000. What is the probability that a randomly selected high school teacher in the town earns less than $50,000?

1) 0.3085
2) 0.6915
3) 0.6915
4) 0.3085

Answer 1

To find the probability that a randomly selected high school teacher in the town earns less than $50,000, we calculate the z-score using the formula z = (x - mean) / standard deviation. Then, we use the z-table to find the corresponding probability. Subtracting this probability from 1 gives the final answer.

Step-by-step explanation:

To find the probability that a randomly selected high school teacher in the town earns less than $50,000, we need to calculate the z-score and then use the z-table to find the corresponding probability. The z-score formula is:

z = (x - mean) / standard deviation

where x is the value we want to find the probability for, mean is the average salary, and standard deviation is the standard deviation of the salaries. In this case, x is $50,000, mean is $43,000, and standard deviation is $18,000.

Plugging these values into the formula:

z = (50,000 - 43,000) / 18,000 = 0.3889

Now, we look up the z-score of 0.3889 in the z-table and find the corresponding probability, which is approximately 0.6508. However, the question asks for the probability of earning less than $50,000, so we need to subtract this probability from 1 to get the final answer:

1 - 0.6508 = 0.3492

Therefore, the probability that a randomly selected high school teacher in the town earns less than $50,000 is approximately 0.3492.