A perfume bottle is designed to have a capacity of 15 ounces.There is variation in the bottle manufacturing process.Based on historical data,let's suppose that the bottle capacity can be reasonably modeled by a normal distribution with a mean of 15 ounces and a standard deviation of 0.2 ounces.What proportion of these bottles will have a capacity between 14.7 and 15.1 ounces?
A)0.3830
B)0.6247
C)0.8664
D)0.9876

Question

Quizplus · Accepted Answer

We need to find the area under the normal distribution curve between 14.7 and 15.1 ounces. 
First, we need to standardize both values:

z1 = (14.7 - 15) / 0.2 = -1.5
z2 = (15.1 - 15) / 0.2 = 0.5

Now, we can use a standard normal distribution table or calculator to find the area between these two z-values:

P(-1.5 < Z < 0.5) = 0.6247

Therefore, approximately 62.47% of the perfume bottles will have a capacity between 14.7 and 15.1 ounces.

A Perfume Bottle Is Designed to Have a Capacity of 15