A gun shop sells gunpowder. Monthly demand for gunpowder is normally distributed, averages 20 pounds, and has a standard deviation of 2 pounds. The shop manager wishesto stock gunpowder inventory at the beginning of each month so that there is only a 2%chance that the shop will run out of gunpowder (i. e., that demand will exceed inventory) in any given month. Calculate the amount of gunpowder to stock in inventory, in pounds.

(A) 16 (B) 23 (C) 24 (D) 32 (E) 43

Question

Kaelyn Reese

Mathematics

10 August, 21:07

A gun shop sells gunpowder. Monthly demand for gunpowder is normally distributed, averages 20 pounds, and has a standard deviation of 2 pounds. The shop manager wishesto stock gunpowder inventory at the beginning of each month so that there is only a 2%chance that the shop will run out of gunpowder (i. e., that demand will exceed inventory) in any given month. Calculate the amount of gunpowder to stock in inventory, in pounds.

(A) 16 (B) 23 (C) 24 (D) 32 (E) 43

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Answers (1)

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Joy · Answer 1

Option (C) 24

Step-by-step explanation:

Let the random variable denoting the amount of gunpowder in the shop be 'x'.

x ~ N (20, 2) i. e. (x-20) / 2 ~ (0, 1)

Let 'a' be the amount (in pounds) of gunpowder to stock in inventory.

Thus, P (x
i. e. P[ (x-20) / 2< (a-20) / 2] = 0.98

i. e. ф [ (a-2) / 2] = 0.98

i. e. (a-20) / 2 = ф⁻¹ (0.98) = 2.054

i. e. a = 20 + (2 * 2.054) = 24.108 ≈ 24 pounds

24 pounds of gunpowder to stock in inventory.

Option (C) 24