MBA5008 Quantitative Analysis & Decision Making SU01 Test: Week 3 Quiz This Ques

Question

MBA5008 Quantitative Analysis & Decision Making SU01 Test: Week 3 Quiz This Question: 12 pts Anticipated consumer demand in a restaurant for free range steaks next month can be modeled by a normal random variable with mean 1,600 pounds and standard deviation 90 pounds a. What is the probability that demand will exceed 1,400 pounds? b. What is the probabillity that demand will be between 1,500 and 1,700 pounds? c. The probability is 0.10 that demand will be more than how many pounds? Click the icon to view the standard normal table of the cumulative distribution function. a The probablity that demand will exceed 1,400 pounds is © Round to four decimal places as needed) b The probability that demand will be between 1,500 and 1,700 pounds is (Round to four decimal places as needed) C. The probability is 0 10 that demand wil be more than pounds (Round to one decimal place as needed ) Enter your answer in each of the answer boxes OType here to search

Explanation / Answer

Lets normalize the variable using params of nomral distribution :

a. P(X>1400) = P(Z> (1400-1600)/90) = P(Z>-2.22) = .9869

b. P(1500<X<1700) = P(1500-1600/90 <Z< 1700-1600 / 90) = P(-1.11<Z<1.11) = .86674 - .13326 = .7335

c. P(X<c) = .10

(c-1600)/90 = 1.28

c = 1.28*90+1600 = 1715.2 pounds.

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