Question

The average teacher's salary in North Dakota is $35,441. Assume a normal distribution with =σ$5100. Round the final answers to at least 4 decimal places and round intermediate z-value calculations to 2 decimal places.What is the probability that a randomly selected teacher's salary is greater than $37,800?=P>X37,800

Answer 1

ANSWER

0.3228

EXPLANATION

We want to find,

$P(X>37800)$

But since X is normally distributed, we have to find the z-score for a standard normal distribution,

$z=\frac{x-\mu}{\sigma}=\frac{37800-35441}{5100}\approx0.46$

So the probability we can find in the standard normal distribution table is,

$P(Z>0.46)$

In the z-score table, we have to find z = 0.46,

The table shows the probability that z is less than that value. We want to find the probability that z is greater than that value. This is,

$P(Z>0.46)=1-P(Z<0.46)=1-0.6772=0.3228$

The probability that a teacher's salary is greater than $37,800 is 0.3228.