Question

Salaries for teachers in a particular elementary school district are normally distributed with a mean of $44,000 and a standard deviation of $6,500. We randomly survey ten teachers from that district.

(a). Find the 90th percentile for an individual teacher’s salary. (Round to the nearest whole number)

(b)  Find the 90th percentile for the average teacher’s salary. (Round to the nearest whole number)

Answer 1

Selutiom lind ave do he a Hene Coram fercenste twe in dividual eachen's Salay 2 e (2.28) 090 have we 2 yonhe giuen data e hae 6500 8320 ko0 2 havedond the b) Hone we Percentile he awerage deacher's Salaty whene nzto P(220.0 o.0

2 .2)6500/10koo0 (1. 2g) 20is.48)tkcoo z 2631.olu leuooo 466 31.0144 2 (4663

Answer 2

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.