. Suppose annual salaries for sales associates from a particular store have a me
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Question
. 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 less than $27,500.
Explanation / 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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