A plant manager knows that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a standard deviation of 20.What percentage of the time will the number of boxes received weekly be between 180 and 210?
A)69.15%
B)19.15%
C)53.28%
D)15.87%

Question

Quizplus · Accepted Answer

We need to find the percentage of boxes received weekly between 180 and 210. 
First, we need to standardize these values using the formula: 
z = (x - μ) / σ  
where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

For x = 180:  
z = (180 - 200) / 20 = -1

For x = 210: 
z = (210 - 200) / 20 = 0.5

Using a standard normal distribution table or calculator, we can find the probabilities for these z-values:

P(z < -1) = 0.1587  
P(z < 0.5) = 0.6915

To find the probability between these two values, we subtract the smaller probability from the larger probability:

P(-1 < z < 0.5) = P(z < 0.5) - P(z < -1) = 0.6915 - 0.1587 = 0.5328

Therefore, the percentage of time the number of boxes received weekly will be between 180 and 210 is 53.28%, which is option C.

A Plant Manager Knows That the Number of Boxes of Supplies