Suppose x has a binomial probability distribution with n = 200 and p = 0.60.  Use the normal approximation to the binomial to find P (X 

The owner of a herd of cows wants to determine the influence of the ages of his cows on the amount of calving difficulty that occurs in his herd.  He constructs the following table:                             Age of Cow (in years)                                           0-2     3-5     6-10     over 10   Total No difficulty     40      35       20          5            100 Difficult birth   35      45       15          5            100 Total                  75      80       35        10           200   What is the probability that a randomly selected cow either has calving difficulty or is less than 3-years-old?

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 75 inches and the sample standard deviation is 8 inches.  Construct a 90% confidence interval for the population mean (μ).  Assume that any necessary assumptions have been met.

According to a study conducted at a university, many adults have experienced lingering “fright” effects from a scary movie or TV show they saw as a teenager.  In a survey of 150 college students, 39 said that they still experience “residual anxiety” from a scary movie or TV show. Perform the calculations needed to determine if the sample size of n = 150 is large enough for large-sample confidence interval procedures to be valid.  Is the sample size large enough?

Suppose x has a binomial probability distribution with n = 200 and p = 0.70.  We want to determine if it is appropriate to use the normal approximation to the binomial.  Which one of the following statements is true?

The average height cows of a certain breed is 54 inches and the standard deviation of the heights is 8 inches.  Fifteen percent of the cows are expected to be less than X inches tall.  Find the value of X.

A swine producer reads a report stating that the average litter size in the US is 7.8 pigs per litter.  However, he feels that the average litter size on his farm is not 7.8 pigs/litter (he wants to detect departure in either direction from the hypothesized mean of 7.8 pigs/litter).  To test his hypothesis, he reviews his records for the past year and randomly selects 16 litters, which averaged 8.0 pigs/litter.  The standard deviation is 1 pig/litter. Does the sample obtained by the producer provide sufficient evidence to reject the null hypothesis?  Explain.

The owner of Get-A-Way Travel has recently surveyed a random sample of 385 customers of the agency.  He would like to determine if the mean age of the agency’s customers is over 31 years.  If so, he plans to alter the destination of their special cruises and tours.  If not, no changes will be made.  He therefore wants to test:    Ho:  μ = 31 years    Ha:  μ > 31 years If he concludes that the mean age is not over 31 years when in fact it is over 31 years, he makes a ________ error.

The symbol for the variance of a population is _______.

Breeders of the Longhorn breed of cattle select to increase the length of the horns (i.e., the distance from the tip of one horn to the tip of the other horn).  A Longhorn breeder would like to know the average length of horns found on Longhorn cattle in Texas.  A random sample of 144 Longhorn cattle yields a mean horn length of 70 inches and a standard deviation of 10 inches. Estimate the population mean for length of horns of Longhorn cattle in Texas using a point estimate.