Question

Assume that the salaries of elementary school teachers in the united states are normally distributed with a mean of $32,000 and a standard deviation of $3000. if 100 teachers are randomly selected, find the probability that their mean salary is less than $32,500.

Answer 1

Answer: 0.9525

Step-by-step explanation:

Given : The salaries of elementary school teachers in the united states are normally distributed with a mean of $\mu=\ 32,000$ and a standard deviation of $\sigma=\ 3000$.

Sample size : n= 100

Let x be a random variable that denotes the salaries of elementary school teachers in the united states.

Formula : $z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

Then, the probability that their mean salary is less than $32,500 will be :-

$P(x$

Hence, the probability that their mean salary is less than $32,500 = 0.9525

Answer 2

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