Question

The monthly demand for a product is normally distributed with mean of 1200 units and standard deviation of 200 units.

1. Find the probability that demand in a given month is between 1020 and 1377 units.

The potential answers are:

A: 78.3%

B: 38.2%

C: 67.5%

D: 62.8%

E: 69.3%

2. If at the beginning of a month 1424 units are stocked, what is the probability that demand exceeds this amount (experiencing stock-out)?

The potential answers are:

A: 20.6%

B: 13.1%

C: 6.1%

D: 1.4%

E: 3.4%

3. If we want to set the probability of stock-out at 6%, how many units shall we have in stock at the beginning of the month?

The potential answers are:

A: 1696

B: 1629

C: 1511

D: 1867

E: 2211

please help asap! by using excel formula.

This is for SOM. THank you!

Answer 1

Solution:

Given in the question

Mean = 1200

Standard deviation = 200

Solution(a)

P(1020<X<1377) = P(X<1377) - P(X<1020) =

Here we will use standardized Z score formula

Z = (1377-1200)/200 = 0.885

Z = (1020-1200)/200 = -0.9

From Z table we found p- value

P(1020<X<1377) = 0.812 - 0.1841 = 0.6279 or 0.628

So its answer is D. I.e. 62.8%

Solution(b)

P(X>1424) = 1- P(X<=1424)

Z = (1424-1200)/200 = 1.12

From Z table we found p-value

P(X>1424) = 1- 0.8686 = 0.1314

So its answer is B. I.e. 13.1%

Solution(3)

Here p-value = 0.94

Z score from Z table is 1.555

X = 1200 + 200*1.555 = 1200 + 311 = 1511

So it answer is C. I.e. 1511