SOLUTION: The average height of 1000 students are normally distributed.its mean is 72 inches and standard deviation is 2 feet . find 1) the number of students whose height is more than 70 i

Question 1203226: The average height of 1000 students are normally distributed.its mean is 72 inches and standard deviation is 2 feet . find
1) the number of students whose height is more than 70 inches
2) the number of students whose height will be between 6 feet and 6.5 feet.
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
n = 1000
m = 72 inches
sd = 2 feet * 12 = 24 inches
find:

1) the number of students whose height is more than 70 inches.

z = (70 - 72) / 24 = -2 / 24 = -.08333...
area to the right of that z-score = .5332068191.
multiply that by 1000 to get 533.2068191.
round to 533, since the number of students has to be an integer.

2) the number of students whose height will be between 6 feet and 6.5 feet..

6 feet = 72 inches.
6.5 feet = 78 inches.
the first part you did in inches because they wanted the answer in inches.
this part you can do in feet because they want the answer in feet.
the mean is 72 inchs / 12 = 6 feet
the standard deviation is 24 inches / 12 = 2 feet.

you have 2 z-scores.
the low z-score is z = (6 - 6) / 2 = 0
the high z-score is z = (6.5 - 6) / 2 = .5 / 2 = .25
area to the left of the low z-score is .5
area to the left of the high z-score is .5987062744.
area in between is .5987062744 - .5 = .0987862744.
multiply that by 1000 to get 98.7862744.
round to 99 since the number of students has to be an integer.

youo could have done both parts in inches or in feet and then converted to the appropriate measure at the end.
any one of those ways is appropriate.
just pick the method that works best for you.

Answer by greenestamps(13215) (Show Source): You can put this solution on YOUR website!

I didn't check the numbers in the response from the other tutor....

But, really now. A mean of 72 inches (6 feet) and a standard deviation of 2 feet?! That means a considerable number of students are over 8 feet tall and even some over 10 feet tall....

Are we talking about earthlings here?

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