Another method of identifying an outlier is to investigate whether there is evidence that a value might have come from a population with a mean different from the mean of the population of the other values. Let X and Y represent random variables. X is distributed normally with mean μ, and standard deviation σ, and Y is distributed normally with mean H, and standard deviation σ. Consider 1 randomly selected value of Y and n-1 randomly selected values of X. (b) Consider the difference Y - X. (i) In terms of y and x, what is the mean of the difference Y-X? (ii) In terms of n and σ, what is the standard deviation of the difference Y-X?

5. A quality control engineer found that the inner and outer diameters of their ball bearings, denoted respectively as X and Y, are random variables with E(X|Y = y) = 0.7 – 0.3y inches and Var(X|Y = y) = 0.0004y for all values of y. From his past experience he also knew that the mean and variance of the outer diameters were E(Y) = 0.7 inches, and Var(Y) squared inches. = 0.0001 %3D • (i) What are the conditional random variables, E(X|Y) and Var(X|Y)? • (ii) Find the mean of the inner diameters, E(X). • (ii) Find the variance of the inner diameters, Var(X).

There are two independent random variables X and Y. X has mean 4 and standard deviation , and Y also has mean 4 and standard deviation . A random variable W is the difference between X and Y. That is, W = X - Y. Calculate the mean of W.

A large airline company called Fusion Fly monitors customer satisfaction by asking customers to rate their experience as a 1, 2, 3, 4, or 5, where a rating of 1 means "very poor" and 5 means "very good". The customers' ratings have a population mean of μ = 4.29, with a population standard deviation of a = 1.15. Suppose that we will take a random sample of n=7 customers' ratings. Let x represent the sample mean of the 7 customers' ratings. Consider the sampling distribution of the sample mean x. Complete the following. Do not round any intermediate computations. Write your answers with two decimal places, rounding if needed. (a) Find μ- (the mean of the sampling distribution of the sample mean). H₂=0 X (b) Find o- (the standard deviation of the sampling distribution of the sample mean). 0--0 X

A magazine claims that the mean amount spent by a customer at Burger Stop is greater than the mean amount spent by a customer at Fry World. The results for samples of customer transactions for the two fast food restaurants are shown below. At x = 0.01, can you support the magazine's claim? Assume the population variances are equal. Assume the samples are random and independent, and the populations are normally distributed. Complete parts (a) through (e) below. Burger Stop Fry World X₁ = $11.22 X₂ = $10.59 $₁ = $0.79 $2 = $0.64 n₂ = 10 n₁ = 12 (a) Identify the claim and state Ho and H₂. Which is the correct claim below? O A. "The mean amount spent by a customer at Burger Stop is greater than the mean amount spent by a customer at Fry World." OB. "The mean amount spent by a customer at Burger Stop is equal to the mean amount spent by a customer at Fry World." O c. "The mean amount spent by a customer at Burger Stop is not equal to the mean amount spent by a customer at Fry World." O D.…

A snack company makes packages of grapes and honeydew slices. The weight of an individual package of grapes, G, is approximately Normally distributed with a mean of 3.25 ounces and a standard deviation of 0.91 ounces. The weight of an individual package of honeydew slices, H, is approximately Normally distributed with a mean of 4.51 ounces and a standard deviation of 2.02 ounces. Assume G and H are independent random variables. Let D = G – H. What is the probability that a randomly selected package of grapes weighs more than a randomly selected package of honeydew slices? 0.127 0.230 0.284 0.334

A random sample of size 10 yielded roughly "mound-shaped" data with a sample mean of 63.5 and a sample variance of 60.8. Let (L, OU) be the interval estimate that contains the population mean with 95% probability. Find the width of the interval. That is, find 0 – 0₁. 4.52 5.49 5.58 5.70 9.04 10.99 11.16 11.40 none of the other answers give the correct width