It is believed that nearsightedness affects about 12% of all children. A kindergarten has registered 198 incoming children. Complete parts a) through c). a) Can the central limit theorem be applied to describe the sampling distribution for the sample proportion of children who are nearsighted? Check the conditions and discuss any assumptions you need to make.

As the sample size is large enough, i.e. n = 198 > 30 the central limit theorem can be applied to describe the sampling distribution for the sample proportion of children who are nearsighted.

Step-by-step explanation:

Let the random variable p denote the proportion of children affected by nearsightedness.

The previously known proportion was, p = 0.12.

A random sample of n = 198 children are selected.

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

The standard deviation of this sampling distribution of sample proportion is:

As the sample size is large enough, i.e. n = 198 > 30 the central limit theorem can be applied to describe the sampling distribution for the sample proportion of children who are nearsighted.