Question

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 36 couples. Complete parts​ (a) through​ (c) below.

a. Find the mean and the standard deviation for the numbers of girls in groups of 36 births.

The value of the mean is__ ​(Type an integer or a decimal. Do not​ round.)

The value of the standard deviation is __. ​(Round to one decimal place as​ needed.)

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

Values of ___ girls or fewer are significantly low. ​(Round to one decimal place as​ needed.)

Values of ___ girls or greater are significantly high. (Round to one decimal place as​ needed.)

c. Is the result of 32 girls a result that is significantly​ high? What does it suggest about the effectiveness of the​ method?

The result is/is not significantly​ high, because 32 girls is greater than/equal to/less than ___ girls. A result of 32 girls would suggest that the method is not effective/is effective.​(Round to one decimal place as​ needed.)

Answer 1

Solution:

Given:

n =number of couples selected = 36

p = probability of a girl = 0.5

Part a) Find the mean and the standard deviation for the numbers of girls in groups of 36 births.

Mean:

Standard deviation :

The value of the mean is = 18

The value of the standard deviation is = 3.0

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

If a value is less than 2 standard deviation below mean then it is significantly low and a value is more than 2 standard deviation above mean then it is significantly high.

Thus find limits for significantly low and significantly high.

A value is significantly low if it is below 12

A value is significantly high if it is above 24

Thus:

Values of 12.0 girls or fewer are significantly low.

Values of 24.0 girls or greater are significantly high.

Part c)  Is the result of 32 girls a result that is significantly​ high? What does it suggest about the effectiveness of the​ method?

The result is significantly​ high, because 32 girls is greater than 24.0 girls.

A result of 32 girls would suggest that the method is effective