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Suppose annual salaries for sales associates from a particular store have a mean of $32,500 and a standard deviation of $2,500
Suppose annual salaries for sales associates from a particular store have a mean of $32,500 and a
standard deviation of $2,500.
a. Calculate and interpret the z-score for a sales associate who makes $36,000.
b. Use Chebyshev's theorem to calculate the percentage of sales associates with salaries between $26,250 and $38,750.
c. Suppose that the distribution of annual salaries for sales associates at this store is bell- shaped. Use the empirical rule to calculate the percentage of sales associates with salaries between $27,500 and $37,500.
d. Use the empirical rule to determine the percentage of sales associates with salaries higher than $37,500.
Expert Solution
Answer:
a.
z= (x-mean)/sd
(36000-32,500)/2500 = 1.4
1.4 standard deviations from the mean, value 0.4192 (+.5 since its above the mean). .9192 salaries below that salary,
b.
(26,250-32,500)/2500 = -2.5 .0054
(38,750-32,500)/2500= 2.5 0.9946
.9946-.0054= .9892
c.
(27,500-32,500)/2500 = -2 ----5
(37,500-32,500)/2500= 2 ---95
this one is easy it follows the 68-95-99.7 rule
so 95-5= 90 %within the rang
d.
we did it above, 5% of people less than that value
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