A sample of concrete specimens of a certain type is selected, and the compressiv

Question

A sample of concrete specimens of a certain type is selected, and the compressive strength of each specimen is determined. The mean and standard deviation are calculated as x = 6000 and s = 400, and the sample histogram is found to be well approximated by a normal curve.

(a)Approximately what percentage of the sample observations are between 5600 and 6400? (Round the answer to the nearest whole number.)
Approximately: %

b)Approximately what percentage of sample observations are outside the interval from 5200 to 6800? (Round the answer to the nearest whole number.)
Approximately (answer is 5 %)

(c) What can be said about the approximate percentage of observations between 5200 and 5600? (Round the answer to the nearest whole number.)
Approximately__ %

i really need to learn how to do this. I understand that you are supposed to subtract 5600-600/400)..... to get -1 < x < 1, however, how do i determine those percentages?

Explanation / Answer

Thing is you should just know the Z tables or know the 68%-95%-99% rule, which says that if you move 1 , 2 or 3 deviation away from mean then u cover 68%-95%-99% of the area under curve.

Lets solve this to understand the above. Please replicate the solution using Z tables, learning that is more important.

5600 and 6400 are 1 deviation from mean

i.e. 6000+/-400

a) Hence between 5600 and 6400 , there are 68% of data ( since i know that 1 dtdev from
mean there is 68% ofdata)

b) This is about 2 stdev from mean. Which means that 95% of data points inside this 5200 to 6800 limit. Hence, 5% is outside the limits

c)This is about 2 stdev from mean. Which means that 95% of data points inside this 5200 to 6800 limit.

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