Would like help solving

Central Limit Theorem Conditions (for proportions):

Condition 1: The sample we have taken is random and independent.

Condition 2: The sample size, n, is large enough to expect at least 10 successes and 10 failures.

Condition 3: The populations is at least 10 times the sample size. 10.

If we take a sample and all of the above conditions hold, then the distribution of the sample proportion is normal with a mean equal to the population proportion (or sample proportion if we don't know it) and a standard deviation equal to the standard error (or standard error estimate).

Variables:

p = the proportion of the population who fits in the group we care about (not always known)

= the proportion of our sample who fits in the group we care about

Standard Error Calculations = (1) / = (1) /

2. Suppose we flip a coin, and we are interested in the proportion of the time that the coin comes up heads.

A) Suppose we flip the coin 100 times. Does this satisfy the 3 conditions of CLT? If so, draw the sampling distribution below.

B) What is the probability of finding a sample that has a proportion of heads that is higher than 60%?

C) Suppose we flip the coin 200 times. Draw the sample distribution below. What is the difference between our distributions in A and C?

D) What is the probability of finding a sample that has a proportion of heads that is higher than 60%?