population of values has a normal distribution with \( \mu=247.9 \) and \( \sigma=53.8 \). You intend raw a random sample of size \( n=54 \). ind the probability that a single randomly selected value is greater than 269.9 . Find the probability that a sample of size \( n=54 \) is randomly selected with a mean greater than 269.9 . \( P(\bar{x}>269.9)=\square \) 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.

Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.52 and a standard deviation of 0.41 . Using the empirical rule, what percentage of the students have grade point averages that are greater than 3.34 ? Please do not round your answer. Answer How to enter your answer (opens in new window)

A water bottling facility has a mean bottling rate of 34.1 thousand bottles per hour with a standard deviation of 2.13 thousand bottles. A nearby cola bottling facility has a mean bottling rate of 25.7 thousand bottles per hour with a standard deviation of 1.63 thousand bottles. One Wednesday from noon to \( 1: 00 \) p.m., the water bottling facility bottled 37.2 thousand bottles of water, and the cola bottling facility bottled 27.7 thousand bottles of cola. Which facility increased their efficiency more during that hour? Answer

The grades on the second statistics test for Ms. Rose's class are in the following list. Find the frequency distribution for the grades. \[ \text { F, D, F, B, F, A, C, F, C, F, D, B, B, B, C, C, F, C, F, D, A } \]

Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.06 and a standard deviation of 1.52 . Using the empirical rule, what percentage of American women have shoe sizes that are greater than 9.58 ? Please do not round your answer.

The grades on the second statistics test for Mr. Brown's class are in the following list. Find the frequency distribution for the grades. \[ \text { C, D, B, F, B, A, F, F, B, B, B, F, D, B, F, D, F, B, F, B, C } \]