Salaries for teachers in a particular elementary school district are normally distributed with a mean of $48,000 and a standard deviation of $5,400. We randomly survey ten teachers from that district. (Round your answers to the nearest dollar.) (a) Find the 90th percentile for an individual teacher's salary.

The 90th percentile for an individual teacher's salary is $54,912.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Find the 90th percentile for an individual teacher's salary.

This is the value of X when Z has a pvalue of 0.9. So it is X when Z = 1.28.

The 90th percentile for an individual teacher's salary is $54,912.

hello from mrbilldoesmath!

answer:

the domain is the set { -2, 0, 2, 3}

discussion:

the domain is the set of x values in the ordered pairs (x,y). taking the x, or first component, of each ordered pair gives   -2, 0, 2, 3.

you,

mrb