Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a​ girl, but assume that the method has no​ effect, so the probability of a girl is 0.5. Assume that the groups consist of 42 couples. Complete parts​ (a) through​ (c) below.a. Find the mean and the standard deviation for the numbers of girls in groups of 48 births.b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high.c. Is the result of 42 girls a result that is significantly​ high? What does it suggest about the effectiveness of the​ method?

Question
Asked Oct 14, 2019

Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a​ girl, but assume that the method has no​ effect, so the probability of a girl is 0.5. Assume that the groups consist of 42 couples. Complete parts​ (a) through​ (c) below.

a. Find the mean and the standard deviation for the numbers of girls in groups of 48 births.

b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high.

c. Is the result of 42 girls a result that is significantly​ high? What does it suggest about the effectiveness of the​ method?

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Expert Answer

Step 1

a.

Let X is random variable denotes the number of girls’ birth follows the binomial distribution.

The probability of a girl is 0.5 and the group consists of 42 couples.

The mean for the number of girls in group of 48 births is 24.

The standard deviation for the number of girls in group of 48 births is 12.

 

That is, p
0.5and n 42
48 (0.5)
=24
Vinp(1-p)
48 (0.5)(0.5)
=12
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That is, p 0.5and n 42 48 (0.5) =24 Vinp(1-p) 48 (0.5)(0.5) =12

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Step 2

b.

The formula for range rule of thumb is given below:

Significantly low ra...

Low range u-20
-24-2 (12)
=0
High range L+20
24+2(12)
=24 24
= 48
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Low range u-20 -24-2 (12) =0 High range L+20 24+2(12) =24 24 = 48

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