SOLUTION: Suppose annual salaries for sales associates from Geoff's Computer Shack have a mean of $32,500 and a standard deviation of $2,500. d. Use the empirical rule to determine the perc

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Question 1196614: Suppose annual salaries for sales associates from Geoff's Computer Shack have a mean of $32,500 and a standard deviation of $2,500.
d. Use the empirical rule to determine the percentage of sales associates with salaries less than $27,500.
I only need help with (d), but I included the other questions and my answers below, in case they are needed to solve the problem.
a. Calculate and interpret the z-score for a sales associate who makes $36,000.
answer: (36000-32500)/2500=1.4
b. Use Chebyshev's theorem to calculate the percentage of sales associates with salaries between $26,250 and $38,750.
26,250-32,500/2,500= -2.5
38,750-32,500/2,500= 2.5
(1-1/z^2)= 1-(1/2.5)^2=1-0.4^2=0.84*100=84%
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.
37,500-32,500/2,500=-2
27,500-32,500/2,500=2
According to the empirical rule, since the answer is between +/-2, then it is 95%.
d. Use the empirical rule to determine the percentage of sales associates with salaries less than $27,500.
I am not sure if I need to pick a number less than 27,500 to try and solve the problem.
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!

Hi
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.
37,500-32,500/2,500 = 2
27,500-32,500/2,500 = -2  ***
According to the empirical rule, since the answer is between +/-2, then it is 95%.

d. Use the empirical rule to determine the percentage of sales associates with salaries less than $27,500.
27,500-32,500/2,500 = -2
"between +/-2 is 95%",  leaving a total of 5% for either side of bell shape curve
% of sales associates with salaries less than $27,500 is 5%/2 = 2.5%

Wish You the Best in your Studies.


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