Suppose x has a distribution with = 11 and o = 6. LUSE SALT (a) If a random sample of size n = 44 is drawn, find and P(11 ≤ x ≤ 13). (Round o to two decimal places and the probability to four decimal places.) ox= P(11 ≤ x ≤ 13) = (b) If a random sample of size n = 62 is drawn, find , and P(11 ≤ x ≤ 13). (Round a to two decimal places and the probability to four decimal places.) 0 x ox= P(11 ≤ x ≤ 13) =

Suppose a simple random sample of size n = 200 is obtained from a population whose size is N=20,000 and whose population proportion with a specified characteristic is p=0.8. Complete parts (a) through (c) below. A. Approximately normal Decause ns. and per-p) 1. OB. Not normal because n ≤0.05N and np(1-p) 0.81)? P(p≥ 0.81)= 3632 (Round to four decimal places as needed.) (c) What is the probability of obtaining x= 150 or fewer individuals with the characteristic? That is, what is P(p ≤ 0.75)? P(p ≤ 0.75)= (Round to four decimal places as needed.) + example Get more help. alues % 5 A + 6 MacBook Pro & 7 * 00 8 Vi I, Clear all ( 9 More Check answer X

The Central Limit Theorem (CLT) says O Samples of size 15 are large enough for the CLT to apply for any populations. O As the sample size increases, the sampling distribution of the mean will get closer and closer to a normal distribution. O Regardless of the sample size, the sampling distribution of the mean is always close to a normal distribution. O Only for symmetric population distributions, the sampling distribution of the mean will get close to a normal distribution as the sample size increases.

Suppose a sample of size n is drawn from a population where the population standard deviation is known. In order to use the Central Limit Theorem, we would have to know that A   n > 30 B   The population is normally distributed. C   n > 30 OR the population is normally distributed D   n > 30 AND the population is normally distributed

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Assume that the height, X, of a college woman is a normally distributed random variable with a mean of 65 inches and a standard deviation of 3 inches. Suppose that we sample the heights of 180 randomly chosen college women. Let M be the sample mean of the 180 height measurements. Let S be the sum of the 180 height measurements. All measurements are in inches. Using R and write the code out.a) What is the probability that X < 59? b) What is the probability that X > 59? c) What is the probability that all of the 180 measurements are greater than 59? d) What is the expected value of S? e) What is the standard deviation of S? f) What is the probability that S-180*65 >10? g) What is the standard deviation of S-180*65 h) What is the expected value of M? i) What is the standard deviation of M? j) What is the probability that M >65.41? k) What is the standard deviation of 180*M? l) If the probability of X > k is equal to .3, then what is k?