Please read the bold portion at the bottom as that is where

Please read the bold portion at the bottom as that is where I am having trouble with this question.

the average annual salary for all U.S. teachers is $47,750. Assume that the distribution is normal and the standard deviation is $5680. Find the probability that a randomly selected teacher earns.

a.) Between $35,000 and $45,000 a year.

b.) More than $40,000 a year

*I understand how to get the z values (like in part a you get z=-2.24 and z=-0.48), but once you have those values how do you satisfy

P( -2.24 < z < -0.48) ? My solution says that equals (0.3156 - 0.0125), but I\'m unsure of how to get these numbers.

Solution

a.) Between $35,000 and $45,000 a year.

P(35000<X<45000) = P((35000-47750)/5680<(X-mean)/s <(45000-47750)/5680)

=P(-2.24<Z<-0.48)

= P(Z<-0.48) - P(Z<-2.24)

=0.3156 - 0.0125

=0.3031 (from standard normal table)

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b.) More than $40,000 a year

P(X>40000) = P(Z>(40000-47750)/5680)

=P(Z>-1.36) = 0.9131 (from standard normal table)