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Chapter 8: Q. 85 (page 482)

The Ice Chalet offers dozens of different beginning ice-skating classes. All of the class names are put into a bucket. The 5 P.M., Monday night, for ages 8to 12, the beginning ice-skating class was picked. In that class were 64girls and 16boys. Suppose that we are interested in the true proportion of girls, ages 8to 12, in all beginning ice-skating classes at the Ice Chalet. Assume that the children in the selected class are a random sample of the population.

State the estimated distribution of P'. Construct a 92% Confidence Interval for the true proportion of girls in the ages 8-12 beginning ice-skating classes at the Ice Chalet.

Short Answer

Expert verified

With a mean of 0.80and a variance of 0.002, follows the normal distribution. is the confidence interval for the given condition.

Step by step solution

01

Given information

Total number of children =80

Total number of girls =64

Total number of boys =16

02

Explanation

There are 80children in this question, 64of them are girls and 16of whom are boys.

p'=0.80and n=80are the values we have.

Will follow a Normal distribution with a mean of 渭equal to 'p'and

a variance of 蟽2=p'(1-p')n

Now, according to the specifications of the query, there is a normal distribution with a mean of 0.80and a variance of 0.80(1-0.20)80=0.002.

Confidence interval =p卤Za2脳p(1-p)n

=0.80卤Z0.082脳0.80脳0.2080=0.80卤1.7507脳0.80脳0.2080=[0.7217,0.8783]

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