A. Weekly sales of Campbell’s soup at a certain grocery store is Normally distri

Question

A. Weekly sales of Campbell’s soup at a certain grocery store is Normally distributed with the average of 1,270 cans and the standard deviation of 250 cans. Find the 80th percentile of weekly sales of Campbell’s soup at this store. Such information is useful in determining levels of orders and stock.

B. The daily demand for unleaded gasoline at a certain gas station is Normally distributed with the average of 18,210 gallons and the standard deviation of 1,460 gallons. Find the value that separates top 25% of the amounts of unleaded gasoline demanded daily at this gas station.

C. There is a 25% chance that a prospective employer will check an educational background of a job applicant. Answer the following questions. (Hint: use Normal distribution as an approximation to the Binomial distribution).

D. For 54 randomly selected job applicants, find the probability that at most 21 of them will have their educational background checked.

E. For 49 randomly selected job applicants, find the probability that at least 18 of them will have their educational background checked.

Explanation / Answer

a) for 80th percentile ; zscore =0.8416

hence 80th percentile of weekly sales =mean +z*Std deviation=1270+0.8416*250=1480.41

b)for top 25% ; z =0.6745

hence  value that separates top 25% of the amounts of unleaded gasoline demanded daily at this gas station

=mean +z*Std deviation= 18210+0.6745*1460=19194.755

d)

here mean =np=54*0.25=13.5

and std deviaiton =(np(1-p))1/2 =3.1819

probability that at most 21 of them will have their educational background checked =P(X<=21)

=P(Z<(21.5-13.5)/3.1819)=P(Z<2.5142)=0.9940

e) for n=49;

mean =np=12.25

and std deviaiton =(np(1-p))1/2 =3.031

probability that at least 18 of them will have their educational background checked =P(X>=18)=1-P(X<=17)

=1-P(Z<(17.5-12.25)/3.031)=1-P(Z<1.7321)=1-0.9584 =0.0416

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