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Toyota would like to know how many miles per gallon the average person gets when driving the hybrid Toyota Prius.  A random sample of 225 drivers yields a mean of 50 mpg and a standard deviation of 7.5 mpg.  Find the 90% confidence interval for the population mean for the miles per gallon of the Toyota Prius.

An animal scientist wants to determine the degree of association between carcass quality grade (variable X) and selling price per pound of carcass (variable Y).  The data for a random sample of 10 Angus steer carcasses are shown in the following table. Quality grade, X Carcass price per pound, Y 5 $1.09 7 1.19 4 0.99 5 1.04 8 1.21 6 1.18 4 0.94 7 1.15 8 1.23 6 1.12 The animal scientist performs a hypothesis test using a significance level of 0.05 to determine if the correlation between carcass quality grade and carcass price per pound is greater than zero. Ho:  

Assume that 20% of all pigs die between birth and weaning.  In a random sample of 200 births, let X be the number of pigs that die between birth and weaning.  Using the normal approximation to the binomial, find the approximate probability that the number of pigs in the sample of 200 that die between birth and weaning is greater than or equal to 50.

Consider the probability distribution shown below for the random variable X:                                                                                                     X             10           20           30           40           50           60      P (X)     0.05        0.20        0.30         0.25        0.10         0.10      Graph P (X).  Locate μ and μ ± 2 σ on the graph.  What is the probability that X will fall within this interval?

A litter of 5 pigs is produced.  What is the probability that exactly 3 of the 5 pigs will be females, assuming that the probability of a male pig is 1/2 and the probability of a female pig is 1/2?

A human gene carries a certain disease from the mother to the child with a probability rate of 60% (i.e., there is a 60% chance that a given child will have the disease).  Suppose a female carrier of the gene has 3 children. Assume that the infections of the 3 children are independent of one another.  What is the probability that all 3 children will get the disease from their mother?

Suppose we want to estimate the average height of all young growing maple trees found on a certain nursery.  We select a random sample of 25 trees and measure their heights.  The sample mean is 70 inches and the sample standard deviation is 10 inches.  Construct a 90% confidence interval for the population mean (μ).  Assume that any necessary assumptions have been met.

Assuming that n1 = n2, find the sample sizes needed to estimate (μ1 – μ2) correct to within 2.5 with probability 0.90.  From prior experience we know that σ1 = 18 and σ2 = 16.

The average weight of a kennel of dogs is 40 lb and the standard deviation of the weights is 5 lb.  Find the probability that a randomly selected dog will weigh between 44 and 48 lb.

Health care issues are receiving a greal deal of attention in both the academic and political arenas.  A sociologist recently conducted a survey of senior citizens whose net worth is too high to quality for Medicaid, but who have no private health insurance.  The ages (in years) of 9 uninsured senior citizens were as follows: Senior Citizen Age 1 65 2 70 3 64 4 84 5 74 6 72 7 87 8 79 9 80 Find the range for the ages of these 9 senior citizens.