If the heights within a certain subpopulation of people are normally distributed with a mean of 180 centimeters and a standard deviation of 10 centimeters, what proportion of the people is shorter than 195 centimeters? Z=(score-mean)/SD

after finiding the proportion i looked at the "areas under the normal curve" in my book. T
The proportion to my problem was 1.5
The book gives me theanswers of .4332 or .0668....which is the correct answer and how can it be determined ?

There is only one answer and it must be greater than 0.500, since 195 exceeds the mean.

The answer (for Z = 0 to 1.5) is 0.9322. Either "the book" is wrong, or you incorrectly typed 0.9322 as 0.4322

To determine the proportion of people shorter than 195 centimeters, you can use the Z-score formula:

Z = (x - mean) / standard deviation

where x is the value we want to find the proportion for (195 centimeters in this case), mean is the mean height (180 centimeters), and standard deviation is the standard deviation of the heights (10 centimeters).

So, in this case, we can calculate the Z-score as follows:

Z = (195 - 180) / 10
Z = 15 / 10
Z = 1.5

Now, to find the proportion of people shorter than 195 centimeters, we need to look up the corresponding area under the standard normal curve. This area represents the proportion of the population that falls below a certain Z-score.

You mentioned that your book provides the answers of 0.4332 or 0.0668. This means that the book is giving you the area to the left or right of the Z-score, not the proportion itself.

If you want to find the proportion of people shorter than 195 centimeters, you need to find the area to the left of the Z-score of 1.5.

To find this area, you can use a standard normal distribution table or a calculator with a built-in normal distribution function. This area represents the probability of a random observation falling below a Z-score of 1.5.

Using either method, you will find that the area to the left of the Z-score of 1.5 is approximately 0.9332. This means that approximately 93.32% of the people in the subpopulation are shorter than 195 centimeters.

Therefore, the correct proportion of people shorter than 195 centimeters is approximately 0.9332, not 1.5.

Note: It's important to understand the context when interpreting the proportion. In this case, the proportion represents the probability of randomly selecting a person from the subpopulation and them being shorter than 195 centimeters.