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batmandillon21
07.03.2020 •
Mathematics
The annual salaries of employees in a large company are approximately normally distributed with a mean of $50,000 and a standard deviation of $20,000.
a.What percent of people earn less than $40,000?
b.What percent of people earn between $45,000 and $65,000?
c.What percent of people earn more than $70,000?
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Ответ:
a) 30.85% of people earn less than $40,000
b) 37.21% of people earn between $45,000 and $65,000.
c) 15.87% of people earn more than $70,000
Step-by-step explanation:
Problems of normally distributed samples are 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:
a.What percent of people earn less than $40,000?
This is the pvalue of Z when X = 40000. So
30.85% of people earn less than $40,000
b.What percent of people earn between $45,000 and $65,000?
This is the pvalue of Z when X = 65000 subtracted by the pvalue of Z when X = 45000. So
X = 65000
X = 45000
0.7734 - 0.4013 = 0.3721
37.21% of people earn between $45,000 and $65,000.
c.What percent of people earn more than $70,000?
This is 1 subtracted by the pvalue of Z when X = 70000. So
1 - 0.8413 = 0.1587
15.87% of people earn more than $70,000
Ответ: