Question

What cutoff value bounds the lowest 30% when using a normal model with a mean of 40 and a standard deviation of 4?

What cutoff values bond the middle 71% when using a normal model with a mean of 52 and a standard deviation of 9?

Step 1

Given normal model with mean 40 and standard deviation 4.

With reference to Standard normal table the Z score such that are to its left is 0.3015 is -0.52 and 0.2981 area to the left of Z score -0.53. We can say approximately the Z score for area of 0.30 to its left is average os -0.52 and -0.53, which is -0.525.

Step 2

Using the below mentioned formula of Z score we determine the value of X which is cutoff value which bounds lowest 30%.

The cut off value, which bounds lowest 30% is 37.9

Step 3

Given normal distribution with mean 52 and standard deviation 9.

middle 71% of the normal distribution has 29% on both tails, where each tail equally divided with 14.5% as shown below

With reference to Z table the Z score with 0.14...

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