It is generally believed that nearsightedness affects about 15% of all children. A local elementary school registered 120 incoming kindergarteners.

Note that this scenario is talking about a sampling distribution since this school is a sample of size 120. Therefore, you will need to calculate the standard deviation using a formula before using the normalcdf and invNorm commands.

a) What is the mean of the sampling distribution of all samples like this:

b) What is the standard deviation of the sampling distribution of all samples like this:

Give the formula with values that you entered in your calculator as a way of showing your work:

Give your final answer rounded to 4 decimal places:

c) What is the probability that less than 10% of the incoming kindergarteners are nearsighted?

Give the command and values you used as a way of showing your work:

Give your final answer rounded to 4 decimal places:

d) If this school measures at the 80th percentile for all incoming kindergarten classes of size 120, what proportion of incoming kindergarteners are nearsighted?

Give the command and values you used as a way of showing your work:

Give your final answer rounded to 2 decimal places.