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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.

A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets – Kroger, Giant Eagle, and Meier.  Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets.  In order to reduce item-to-item variation, the prices were recorded for each item on the same day at each supermarket. Item                          Kroger    Giant Eagle    Meier     1) Big Thirst Towel      $1.21       $1.49          $1.59 2) Post Golden Crisp    2.78         2.99            3.35 3) Tylenol Tablets         5.98         5.29            5.98           .                              .              .                   .           .                              .              .                   . 59) Colgate Shave       0.94         1.10            1.19 60) Kidney Beans        0.45          0.56            0.38                                                                                   Identify the dependent (response) variable for this experiment.

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 median age of these 9 senior citizens.

You are interested in purchasing a really good bull to breed your cows.  You look up the sale prices of a sample of 16 bulls that were sold in last year’s National Western Stock Show sale in Denver.  The average sale price was $10,000 with a standard deviation of $1,000.  Estimate the population mean for the sale prices of the bulls using a 95% confidence interval.