Use Info for A and B: The manager of a health food store has determined that the
ID: 3355889 • Letter: U
Question
Use Info for A and B:
The manager of a health food store has determined that the weekly demand, X, for a popular type of granola is a normally distributed random variable with mean 85 pounds and standard deviation 5 pounds.
A. If the manager decides to have 94 pounds of this granola in stock at the beginning of each week, for what percentage of all weeks will the weekly demand exceed the amount in stock?
(a) 96.41% (b) 7.19% (c) 3.59% (d) 91.54% (e) 21.19%
B. if the demand for a given week falls within the lowest 2.5% of all possible values for the weekly demand, the price of the granola will be reduced for the following week. What is the largest value that the weekly demand can assume and still be among the lowest 2.5% of all possilbe values for the weekly demand?
(a)75.200 pounds (b) 94.810 lbs (c)84.875 lbs (d)72.500 lbs (e) 84.994 lbs
Explanation / Answer
A) P(Demand exceed stock)
= P(X > 94)
= P(z > (94 - 85)/5)
= P(z > 1.8)
= 0.0359
= 3.59%
Option C is correct.
B) For lowest 2.5% of the area, z = -1.96
Hence,
Required value = 85 - 1.96*5 = 75.2 pounds
Option A is correct.
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