Question

2.) Use Chebysheff’s Theorem to answer the following

a.) Use the Chebysheff formula and calculate at least what percentage of any population will lie within

K = 2.5 standard deviations of the population mean? (2)

b.) A major sales company has compiled web site data over the last year and has determined that the average number of visits to their website per day is, μ = 30,000 visitors with a standard deviation of
σ = 2500 visitors per day. The marketing manager uses Chebysheff’s theorem and estimates that at least 89% of the time he/she expects the daily number of visitors to the web site to lie in the interval (a, b). Find the endpoints, a & b of the 89% Chebysheff Confidence Interval. (4)

c.) If a visitor to the website spends on average $20 per visit using the results in part b above the manager predicts that at least 89% of the time the daily total sales revenue will lie in the interval ($C, $D).
Find $C and $D. (2)

Answer 1

Ans:

a)

At least percentage of any population will lie within K = 2.5 standard deviations of the population mean

=1-(1/2.5^2)

=0.84 or 84%

b)

0.89=1-(1/k^2)

k=sqrt(1/0.11)=3

a=30000-3*2500=22500

b=30000+3*2500=37500

c)

C=22500*20=450,000

D=37500*20=750,000