(Solved): Given a normal distribution with =50 and =4, and given you select a sample of n=100, a. What is ...

Given a normal distribution with $\mu =50$ and $\sigma =4$, and given you select a sample of $n=100$, a. What is the probability that $\bar{X}$ is less than 49 ? $P(\bar{X}<49)=$ (Type an integer or decimal rounded to four decimal places as needed.) Suppose a random sample of $n=436$ measurements is selected from a binomial population with probability of success $p$. For each of the given values of $p$, give the mean and standard deviati the sampling distribution of the sample proportion, $\hat{p}$. Complete parts a through $\mathbf{c}$ below. a. $p=0.2$ The mean of the sampling distribution of $\hat{p}$ is The standard deviation of the sampling distribution of $\hat{p}$ is (Round to four decimal places as needed.) A population has a proportion equal to 0.40 . Calculate the probabilities below with $n=100$. a. $P(\bar{p}\le 0.42)$ b. $P(\bar{p}>0.45)$ c. $P(0.30<\bar{p}\le 0.45)$ d. $P(\bar{p}\ge 0.37)$ a. $P(\bar{p}\le 0.42)=0.6585$ (Round to four decimal places as needed.) b. $P(\bar{p}>0.45)=0.1537$ (Round to four decimal places as needed.) c. $P(0.30<\bar{p}\le 0.45)=0.8257$ (Round to four decimal places as needed.) d. $P(\bar{p}\ge 0.37)=$ (Round to four decimal places as needed.)