A particular type of plastic soap bottle is designed to have a capacity of 15 ounces.There is variation in the bottle manufacturing process.Based on historical data,suppose that 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

To solve this problem, we need to find the proportion of bottles with a capacity between 14.7 and 15.1 ounces. We can do this by finding the area under the normal distribution curve between these two values.

First, we need to standardize these values using the formula:

z = (x - μ) / σ

where z is the standardized score, x is the value we want to find the proportion for (in this case, 14.7 and 15.1), μ is the mean (15 ounces), and σ is the standard deviation (0.2 ounces).

For 14.7 ounces:

z = (14.7 - 15) / 0.2 = -1.5

For 15.1 ounces:

z = (15.1 - 15) / 0.2 = 0.5

Next, we need to find the area under the normal distribution curve between these two standardized values. We can use a standard normal distribution table or a calculator to find this area.

Using a calculator, we can use the normalcdf() function on a TI-83 or TI-84 calculator or the normdist() function in Excel.

normdist(0.5,0,1) - normdist(-1.5,0,1) = 0.6247

Therefore, the proportion of bottles with a capacity between 14.7 and 15.1 ounces is approximately 0.6247. The best choice is B.

A Particular Type of Plastic Soap Bottle Is Designed to Have