Problem 6BSC

Finding μ, σ, and Unusual Values. In Exercises, assume that a procedure yields a binomial distribution with n trials and the probability of success for one trial is p. Use the given values of n and p to find the mean μ and standard deviation σ . Also, use the range ruh of thumb to find the minimum usual value μ – 2σ and the maximum usual value μ – 2 σ.

Gender Selection In an analysis of preliminary test results from the XSORT gender-selection method, 14 babies are born and it is assumed that 50% of babies are girls, so n = 14 and p = 0.5.

Answer :

Step 1 of 2:

Given, In an analysis of preliminary test results from the XSORT gender-selection method, 14 babies are born and it is assumed that 50% of babies are girls, so n = 14 and p = 0.5.

The procedure yields a binomial distribution.

Where, mean = = np = 14(0.5)

= 7

Variance = npq

= (14)(0.5)(0.5)

= 3.5

Standard deviation = =

= 1.87

Step 1 of 2 :

We have to find the minimum usual value and maximum usual value

i.e , Minimum usual value

= - 2

= 7 - 2(1.87)

= 3.26 are girls

Maximum usual value

= + 2

= 7 + 2(1.87)

= 10.74 are girls