Question 171554This question is from textbook
: I need someone to double check my answer please:
The heights of 1000 girls at East High School were measured, and the mena was found to be 64 inches., with a standard deviation of 2 inches. If the heights are approximately normally distributed, about how many of the girls are between 60 and 64 inches?
I came up with the answer of 0.99997
This question is from textbook
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Notice how 60 inches is 4 inches away from the mean 64 inches. Also, note how 4=2*2 (where the second two is the standard deviation).
So this means that someone who is 60 inches is two standard deviations away from the mean. Since 95% of the population fall within 2 standard deviations (both above and below the mean), this tells us that only half of that (47.5%) lie below the mean.
So only 47.5% of the population has a height of 60 to 64 inches. Now simply multiply 0.475 (the decimal equivalent of 47.5%) by 1000 (the size of the population) to get
0.475*1000=475
So there are 475 girls that are between 60 and 64 inches.
Note: your answer of 0.99997 doesn't make any sense. Why? You cannot have a decimal number of girls. So before any work can be done, we know that the answer must a whole number.
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