You have two large bins of several thousand plastic beads. Bin A is 60% red beads, Bin B is 54% red beads. Suppose you select a random sample of 80 beads from each bin and calculate P the proportion of red beads in the sample from Bin A and P the proportion of red beads in the sample from Bin B. (a) What is the mean and standard deviation of the sampling distribution of PA-P? (b) Calculate the probability that your random sample from bin B has a higher proportion of red beans than your random sample from bin A (c) Should we be surprised if your random sample from bin B has a higher proportion of red beans than your random sample from bin A?

Alex wants to find out: if the standard deviation of the mean for the sampling distribution of random samples of size 256 from a large or infinite population is 9, how large must the sample size become if the standard deviation is to be reduced to 2.7 (or even smaller)?

The mean weekly earnings of all female workers in a state is $710 and the mean weekly earnings of all male workers in the same state is $760. The standard deviations of the weekly earnings are $86 for the females and $106 for the males. Suppose we take one sample of 316 female workers and another sample of 329 male workers from this state.  1.1. By hand, what is the mean of the sampling distribution of the difference between the mean weekly earnings for females and males? 1.2. By hand, what is the standard deviation of the sampling distribution of the difference between the mean weekly earnings for females and males, rounded to two decimal places?

Recent studies have shown that about 16% of American adults fit the medical definition of being obese. A large medical clinic would like to estimate what percentage of their patients are obese, so they take a random sample of 400 patients and find that 52 are obese. Suppose that in truth, the same percentage holds for the patients of the medical clinic as for the general population, 16%.  Find the mean of the sampling distribution of p̂.

In a large section of a statistics​ class, the points for the final exam are normally​ distributed, with a mean of 74 and a standard deviation of 8. Grades are assigned such that the top​ 10% receive​ A's, the next​ 20% received​ B's, the middle​ 40% receive​ C's, the next​ 20% receive​ D's, and the bottom​ 10% receive​ F's. Find the lowest score on the final exam that would qualify a student for an​ A, a​ B, a​ C, and a D. The lowest score that would qualify a student for an A is nothing. ​(Round up to the nearest integer as​ needed.) The lowest score that would qualify a student for a B is nothing. ​(Round up to the nearest integer as​ needed.) The lowest score that would qualify a student for a C is nothing. ​(Round up to the nearest integer as​ needed.) The lowest score that would qualify a student for a D is nothing. ​(Round up to the nearest integer as​ needed.)

A standardized exam’s score are normally distributed. In a recent year, the mean test score was 1477 and the standard was 315. The test scores of four students selected at random 1860 1230, 2160, and 1360. Find the Z- score that correspond to each value and determine wether any of the values are unusual. The Z-score for 1860 is-The Z-score for 1230 is-The Z-score for 2160 is-The Z-score for 1360is-

In 1995, the median price of a PC was $1200. Suppose that a random sample of100 persons who bought their PCs during that year recorded the amount spent (byeach of them) on his/her PC. State the approximate sampling distribution of ˆp, theproportion of persons who spent more than $1200 on a PC. Find the probabilitythat more than 60% of this group spent more than $1200.   NOTE: Please explain each part, so the problem can be used as a Study Guide

A population has a mean p= 75 and a standard deviation o= 6. Find the mean and standard deviation of a sampling distribution of sample means with sample size n= 36. (Simplify your answer.)

A study found that there was 48% chance that the driver fails a breathalyzer test when it is administered on a Friday night. The test is administered to 80 drivers. What distribution that can be used to model the above situation. How many drivers do we expect to fail the test

For a population that has a standard deviation of 22​, figure the standard deviation of the distribution of means for samples of size​ (a)2​, (b)4​, (c)5​ and​ (d)10.