Question 1: A normal distribution has a mean of 50 and a standard deviation of 4.
a. Compute the probability of a value between 44.0 and 55.0.
b. Compute the probability of a value greater than 55.0.
c. Compute the probability of a value between 52.0 and 55.0.
Question 2: The owner of Britten's Egg Farm wants to estimate the mean number of eggs laid per chicken. A sample of 20 chickens shows they laid an average of 20 eggs per month with a standard deviation of 2 eggs per month.
a. What is the value of the population mean? What is the best estimate of this value?
b. Explain why we need to use the t distribution. What assumption do you need to make?
c. For a 95 percent confidence interval, what is the value of t?
d. Develop the 95 percent confidence interval for the population mean.
e. Would it be reasonable to conclude that the population mean is 21 eggs? What about 25 eggs?
Question 3: The National Collegiate Athletic Association (NCAA) reported that the mean number of hours spent per week on coaching and recruiting by college football assistant coaches during the season is 70. A random sample of 50 assistant coaches showed the sample mean to be 68.6 hours, with a standard deviation of 8.2 hours.
a. Using the sample data, construct a 99 percent confidence interval for the population mean.
b. Does the 99 percent confidence interval include the value suggested by the NCAA? Interpret this result.
c. Suppose you decided to switch from a 99 to a 95 percent confidence interval. Without performing any calculations, will the interval increase, decrease, or stay the same? Which of the values in the formula will change?