Question

The Ice Chalet offers dozens of different beginning iceskating classes. All of the class names are put into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In that class were 64 girls and 16 boys. Suppose that we are interested in the true proportion of girls, ages 8 to 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$X.X~\_\_\_\_\_\_\_\_$

Short answer

The estimated distribution of$X$is$X~N(np,\sqrt{npq})$.

Step-by-step solution

Step: Given information

Given in the question that, there are 64 girls and 16 boys in a skating class. Suppose we are interested in the true proportion of girls, ages 8 to 12, in all beginning ice skating classes ate the Ice Chalet.

We have to state the estimated distribution of$X$

Solution

The $X$is an estimated distribution that follows the normal distribution having the parameters of $N(np,\sqrt{npq})$

Where,

$n=$number of trails

$p=$probability of successes

Therefore, the estimated distribution of$X$is$X~N(np,\sqrt{npq})$