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 ?
I have already answered this question, which you posted twice. Apparently your book has a typo error. The correct answer is 0.9332
To find the proportion of people shorter than 195 centimeters, we need to find the area under the normal curve to the left of 195 centimeters.
First, we need to calculate the Z-score, which is a measure of how many standard deviations an individual value is from the mean. The formula for calculating the Z-score is:
Z = (score - mean) / standard deviation
In this case, the score is 195 centimeters, the mean is 180 centimeters, and the standard deviation is 10 centimeters. Plugging in these values, we get:
Z = (195 - 180) / 10
Z = 15 / 10
Z = 1.5
Now, we need to find the proportion of the area under the normal curve to the left of a Z-score of 1.5. We can look up this value in a standard normal distribution table or use a statistical calculator.
Using a standard normal distribution table, we can find that the area to the left of a 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 answer is approximately 0.9332 or 93.32%. The values you mentioned in the book (0.4332 and 0.0668) might be either an error or referring to a different problem.