Answer:
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
has a pvalue of 0.3085.
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
has a pvalue of 0.7734.
X = 45000
has a pvalue of 0.4013.
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
has a pvalue of 0.8413.
1 - 0.8413 = 0.1587
15.87% of people earn more than $70,000