Question

I need the calculation of a female with a height of 5'1.

The average height for all males is 69.3 inches with a standard deviation of 2.8 inches. For females, the average height is 64 inches and the standard deviation is 2.8. These are population values. For this week’s discussion, you will calculate a z-score based on your own height and determine whether your score is within the 95% normal range or if it is out of that range and considered unusual.

Measure your height as precisely as possible to a tenth of an inch. For example, 5’2 ¼” would be 62.3 inches tall. Calculate the z-score based on population values for males or females. Use the formula: z= (x-µ)/σ where x is your height in inches. Calculate the normal range by creating the interval that is within 2 standard deviations of the population mean. Multiply the population standard deviation by 2 and then add/subtract from the population mean.

Answer 1

Answer)

According to the emperical rule

If the data is normally distributed

Then 68% lies in between mean - s.d and mean + s.d

95% lies in between mean - 2*s.d and mean + 2*s.d

99.7% lies in between mean - 3*s.d and mean + 3*s.d

And z = (x - mean)/s.d

Z score is nothing but standard deviations above or below the mean

Female height

Mean = 64.

S.d = 2.8

We are given with the height of 5'1 that is 61 inches

Z = (61 - 64)/2.8 = -1.07

Clearly it is not outside the range as z score is in between -2 and 2