Question

Monthly sales of water heaters are normally distributed with a mean of 21 and a standard deviation of 5. What is the probability of selling 12 water heaters or

less?
a) 3.59%
Ob) 1.8096
O c) 96.41%
O d) 8.45%

Answer 1

Option A: 3.59% is the correct answer

Explanation:

Z-score is used to calculate the probabilities when mean and standard deviation is given.

Given

Mean = μ = 21

SD = σ = 5

We have to find the probability of selling 12 or less water heaters so our x value is 12

x = 12

The z-score of a value is calculated as:

z-score = (x-μ)/σ

Putting the values

`z-score=(12-21)/(5) \\=(-9)/(5)\\=-1.8`

Now z-score table will be used to calculate the probability for z= -1.8

So we will go for the row with -1.8 and column 0, which gives us: 0.03593

As we have to calculate the probability in percentage

`=0.03593*100\\= 3.593\%`

Hence,

Option A: 3.59% is the correct answer