Question

The weekly salaries of elementary school teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. If one elementary school teacher is randomly selected, what is the probability that he/she earns less than $450 a week?

Answer 1

Answer:

The probability is $P(X < 450 ) = 0.18703$

Step-by-step explanation:

From the question we are told that

    The mean is  $\mu = \ 490$

     The standard deviation is  $\sigma = \ 45$

Generally the probability that he/she earns less than $450 a week is mathematically represented as

        $P(X < 450 ) = P(\frac{X - \mu }{\sigma} < \frac{450 - 490}{45} )$

$\frac{X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ X )$

   

          $P(X < 450 ) = P(Z < -0.8889 )$

From the z table  the area under the normal curve to the left corresponding to    -0.8889  is

         $P(Z < -0.8889 ) = 0.18703$

=>     $P(X < 450 ) = 0.18703$