BackHistory Grades In a history class, the grades for various assessments are all positive numbers and have different distributions. Determine whether the grades for each assessment could be normally distributed. Explain your reasoning.
e. an extra credit assignment with a mean of 2.25 and a standard deviation of 2.49
Ice Cream The weights of ice cream cartons are normally distributed with a mean weight of 10 ounces and a standard deviation of 0.5 ounce.
a. What is the probability that a randomly selected carton has a weight greater than 10.21 ounces?
In Exercises 27–32, the random variable x is normally distributed with mean mu=74 and standard deviation sigma=8. Find the indicated probability.
P(x < 55)
In Exercises 21–26, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability.
P(0.42 < z < 3.15)
In Exercises 21–26, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability.
P(z < 1.28)
In Exercises 7–18, find the indicated area under the standard normal curve. If convenient, use technology to find the area.
To the left of z = -1.5 and to the right of z = 1.5
In Exercises 7–18, find the indicated area under the standard normal curve. If convenient, use technology to find the area.
Between z = -1.55 and z = 1.04
In Exercises 7–18, find the indicated area under the standard normal curve. If convenient, use technology to find the area.
To the left of z = -2.825
In Exercises 7–18, find the indicated area under the standard normal curve. If convenient, use technology to find the area.
To the left of z = -1.95
In Exercises 5 and 6, find the area of the indicated region under the standard normal curve. If convenient, use technology to find the area.
In Exercises 1 and 2, use the normal curve to estimate the mean and standard deviation.
Employee Wellness A survey of employed U.S. adults found that only 35% believe their employer cares about their well-being. You randomly select a sample of U.S. employees. Find the probability that fewer than 100 believe their employer cares about their well-being. (Source: Gallup)
c. You select 400 U.S. employees.
Daily Commute About 83% of U.S. employees drive their own vehicle to work. You randomly select a sample of U.S. employees. Find the probability that more than 100 of the employees drive their own vehicle to work. (Source: U.S. Bureau of Labor Statistics)
c. You select 150 U.S. employees.
Approximating a Binomial Distribution In Exercises 17 and 18, a binomial experiment is given. Determine whether you can use a normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why.
Bachelor’s Degrees Twenty-two percent of adults over 18 years of age have a bachelor’s degree. You randomly select 20 adults over 18 years of age and ask whether they have a bachelor’s degree.
Determine whether any of the events in Exercise 33 are unusual. Explain your reasoning.