Question

Women’s heights have a mean of 165 cm and a standard deviation of 6.5 cm.

5. Make up a probability problem in the context of women’s heights that cannot be solved using the 68- 95-99.7 Empirical Rule. Explain why your problem cannot be solved using the Empirical Rule.

Answer 1

Given Information:

Mean = 165 cm

Standard Deviation = 6.5 cm

Make up a probability problem in the context of women's heights that cannot be solved using the 68-95-99.7

Example Problem: Find the probability that the mean height will be less than 160 cm.

Following formula can be used to calculate the probability:

Now, we have to refer to the z table to get the probability value at P (Z<-0.76)

P (Z<-0.76) = 0.2206

The above problem can not be solved by using empirical rule because the empirical rule gives the probability values at standard distributions such as :

P (-1<z<1) - 0.68

P (-2<z<2) - 0.9545

P (-3<z<3) - 0.997

Our z value is -0.76. So, the probability can only be calculated by referring to the z table.

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