Please read the bold portion at the bottom as that is where I am having trouble
ID: 3432135 • Letter: P
Question
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.
Explanation / Answer
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)
---------------------------------------------------------------------------------------------------------
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)
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.