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Chapter 6: Problem 14
For the standard normal distribution, what is the area within three standard deviations of the mean?
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For a binomial probability distribution, \(n=80\) and \(p=.50\). Let \(x\) be the number of successes in 80 trials. a. Find the mean and standard deviation of this binomial distribution. b. Find \(P(x \geq 42)\) using the normal approximation. c. Find \(P(41 \leq x \leq 48)\) using the normal approximation.
According to the U.S. Department of Agriculture, the average American consumed \(54.3\) pounds (approximately seven gallons) of salad and cooking oils in 2008 (www.ers.usda.gov/data/foodconsumption). Suppose that the current distribution of salad and cooking oil consumption is approximately normally distributed with a mean of \(54.3\) pounds and a standard deviation of \(14.5\) pounds. What percentage of Americans' annual salad and cooking oil consumption is a. less than 10 pounds b. between 40 and 60 pounds c. more than 90 pounds d. between 50 and 70 pounds
The pucks used by the National Hockey League for ice hockey must weigh between \(5.5\) and \(6.0\) ounces. Suppose the weights of pucks produced at a factory are normally distributed with a mean of \(5.75\) ounces and a standard deviation of \(.11\) ounce. What percentage of the pucks produced at this factory cannot be used by the National Hockey League?
A charter bus company is advertising a singles outing on a bus that holds 60 passengers. The company has found that, on average, \(10 \%\) of ticket holders do not show up for such trips; hence, the company routinely overbooks such trips. Assume that passengers act independently of one another. a. If the company sells 65 tickets, what is the probability that the bus can hold all the ticket holders who actually show up? In other words, find the probability that 60 or fewer passengers show up. b. What is the largest number of tickets the company can sell and still be at least \(95 \%\) sure that the bus can hold all the ticket holders who actually show up?
What are the parameters of the normal distribution?
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