A population of values has a normal distribution with \( \mu=125.6 \) and \( \sigma=74 \). You intend to draw a random sample of size \( n=11 \). Find the probability that a single randomly selected value is less than 83.2 . \( P(x<83.2)= \) Find the probability that a sample of size \( n=11 \) is randomly selected with a mean less than 83.2 . \( P(\bar{x}<83.2)=0.0287>\sigma^{6} \) Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact \( z \) - scores or \( z \)-scores rounded to 3 decimal places are accepted.

Scores on a test have a mean of 78 and a standard deviation of 13 . Tom has a score of 66 . Convert Tom's score to a \( z \)-score, rounded to the nearest hundredth.

A water bottling facility has a mean bottling rate of 33.5 thousand bottles per hour with a standard deviation of 1.92 thousand bottles. A nearby cola bottling facility has a mean bottling rate of 26.2 thousand bottles per hour with a standard deviation of 1.42 thousand bottles. One Wednesday from noon to \( 1: 00 \) p.m., the water bottling facility bottled 36.8 thousand bottles of water, and the cola bottling facility bottled 28.4 thousand bottles of cola. Which facility increased their efficiency more during that hour? Answer

A water bottling facility has a mean bottling rate of 35.2 thousand bottles per hour with a standard deviation of 2.04 thousand bottles, A nearby cola bottling facility has a mean bottling rate of 26.9 thousand bottles per hour with a standard deviation of 1.51 thousand bottles. One Wednesday from noon to \( 1: 00 \) p.m., the water bottling facility bottled 36.9 thousand bottles of water, and the cola bottling facility bottled 27.9 thousand bottles of cola. Which facility increased their efficiency more during that hour? Answer

Suppose that IQ scores have a bell-shaped distribution with a mean of 95 and a standard deviation of 16 . Describe where the highest and lowest \( 32 \% \) of IQ scores lie. Answer botween 47 and 143 below 79 and above 111

Identify the population, the sample, and any population parameters or sample statistics in the given scenario. In the 1960 s, a poll of 2617 homeowners in the United States resulted in a report that the average price of a house in the U.S. was \( \$ 18,500 \). Answer O Population: none given: Sample: 2617 homeowners polled: Sample Statistic: \( \$ 18,500 \) Opopulation: U.S. homeowners: Sample: none given; Population Parameter: \( \$ 18,500 \)