Agun 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

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<a) = 1 - 0.02 = 0.98

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

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet