Jacob Monroy-Diaz 10/28/23 9:38 AM Question 6, 8.2.RA-1 HW Score: $69.44 \%, 4.17$ of 6 Part 1 of 2 points Points; 0 ol 1 . Save Fill in the blanks to complete the following statements (a) For the shape of the distribution of the sample proportion to be approximately normal, it is required that $n p(1-p) \geq$ (b) Suppose the proportion of a population that has a certain characteristic is 0.7 . The mean of the sampling distribution of $\hat{p}$ from this population is $\mu_{\hat{p}}=$ This is a reading assessment question. Be certain of your answer because you only get one attempt on this question ) (a) For the shape of the distribution of the sample proportion to be approximately normal, it is required that $n p(1-p) \geq$ (Iype an integer or a decimal.) Clear all Check ansuri

Step 1 ：This question is about the Central Limit Theorem (CLT) for proportions. The CLT states that if you have a population with a certain characteristic (like a proportion p), and you take sufficiently large random samples from the population with replacement, then the distribution of the sample proportions will be approximately normally distributed.

Step 2 ：The condition for the sample proportion to be approximately normal is that both np and n(1-p) are greater than or equal to 10. This is a rule of thumb that ensures that the binomial distribution (which is the distribution of the sample proportions) is sufficiently close to the normal distribution.

Step 3 ：For part (b), the mean of the sampling distribution of the sample proportion (often denoted as p-hat) is simply the population proportion, p. This is because the expected value (or mean) of a sample proportion is just the population proportion.

Step 4 ：So, for part (a), the answer should be 10, and for part (b), the answer should be 0.7.

Step 5 ：However, since the question only asks for the first part, I will only provide the answer for part (a).

Step 6 ：Final Answer: \(\boxed{10}\).