Question

25 POINTS!!!!!!!!! ALGEBRA 2 STATISTICS QUESTION!!!!!!!!!!!!!!

A researcher determined that the heights of male students in a particular town are normally distributed with a mean of 65 inches and a standard deviation of 1.7. Use the graph above to answer the following questions:

a. What percentage of these students is taller than 66.7 inches?

b. If the data are based on 300 students, how many students are between 61.6 and 68.4 inches tall? Explain.

Answer 1

A median is 65 inches and a standard deviation is 1.7:
a.   65 + 1 SD = 65 + 1.7 = 66.7 in
It means that there are : 100% - ( 50% + 34% ) = 100% - 84% = 16% students taller than 66.7 inches.
b.  Heights between 61.6 in and 68.7 in are within 2 standard deviations:
13.5% + 34% + 13.5% + 34% = 95%
0.95 * 300 = 285
There are 285 students between 61.6 in and 68.7 in tall. 

Answer 2

a. 65 + 1 SD = 65 + 1.7 = 66.7 in

That means that there are: 100% - ( 50% + 34% ) = 100% - 84% = 16% students taller than 66.7 inches.

b. 13.5% + 34% + 13.5% + 34% = 95%

0.95 * 300 = 285

There are 285 students between the heights of 61.6 in and 68.7 in.