A grocery store sells bread. Some days they have too much bread left at day\'s e

Question

A grocery store sells bread. Some days they have too much bread left at day's end (surplus), while other days they don't carry enough (shortage). The company's daily sales are normal distributed, with mean sales (mu) of 50 loaves, and a standard deviation (sigma) of 10 loaves. If X = # of bread sales in a day, find the following probabilities, using this Normal Distribution Table: a. rho (x greaterthanorequalto 60 = __ b. rho(x lessthanorequalto 42) = __ c. The company wants to order loaves so they will have a shortage only 10% of the time. X = ___ d. The company sells more bread on weekends than the mean. Find rho (X greaterthanorequalto 65 loaves GIVEN it's Saturday)? ___

Explanation / Answer

a. p(x>=60)

z value where mean = 50 and standard deviation = 10

so Z = (60-50)/10 = 1

soP(x>=60) = 1 - (1) = 1- 0.8413 = 0.1587 = 15.87 %

(b) p(X<=42)

Z - value = (42 - 50)/10 = - 0.8

so p(X<=42) = (-0.8) = 0.2119 = 21.19%

(c) Shortage only 10% of the time so let say cutoff value = K

so Pr( X>=K ; 50; 10) = 0.10

Pr( X < K ; 50; 10)= 0.90

so from Z - table, value of Z for the respective p - value = 1.28

so (K-50)/10 = 1.28

K = 50 + 10 * 1.28 = 62.8 loave

(d) Company sell more bread on weekend than the mean value

so Pr (More breads on weekends) = 0.5

and Pr(X>=65; 50;10) = 1 - Pr(X< 65; 50;10)

Z - table = (65 -50)/10 = 1.5

so  Pr(X>=65; 50;10) = 1- (1.5)

so this is the question of conditional probability where

Pr( X>=65; 50;10 where it is saturday) = [1 - (1.5) ] /0.5 = (1- 0.9332)/ 0.5 = 0.1336

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