Exam 7: Continuous Probability Distributions

Grades for a statistics exam for a certain class follow the normal probability distribution with a mean of 82 and a standard deviation of 12.What percentage of the students in the class earned a C grade (70-79)?

Find the z-score that determines that the area to the right of z is 0.8264.

The mean of the exponential distribution is the inverse of that of the normal distribution.

In the normal distribution,the right half of the curve is a mirror image of the _________________________,since the distribution is ____________________.

Describe the method of finding the area under the standard normal curve between z = 0 and z =- 1.33.

Women make up 58% of the U.S.civilian workforce of 124 million.The U.S.Department of Commerce randomly selects 100 workers for a conference on national health care.If there are fewer than 45 or more than 65 females invited,severe political ramifications are possible.What is the probability that the conference planners will be criticized for the representation by women at the conference?

The Independent Bank surveyed the status of student accounts and found that the average overdraft was $21.22 with a standard deviation of $5.49.If the distribution is normal,find the probability of a student being overdrawn by more than $18.75.

A videotape store has an average weekly gross of $1,158 with a standard deviation of $120.Let x be the store's gross during a randomly selected week.If this is a normally distributed random variable,then the number of standard deviations from $1,158 to $1,360 is:

According to the law of large numbers,frequency distributions generated by statistical packages will more closely approach the theoretical distribution from which they were drawn whenever the number of observations becomes larger.

For a Poisson process,the ____________________ distribution describes the continuous random variable x,where x is the amount of time,space,or distance between occurrences of these rare events.

Which of the following distributions is appropriate to measure the length of time between arrivals at a grocery checkout counter?

In 1997,private planes had 1.5 fatal crashes per 100 thousand flying hours.For a continuous random variable with an exponential distribution: What is the probability that the time between the next two crashes will fall between 50 and 70 thousands hours,i.e.P(50 ≤ x ≤ 70); x = thousands of flying hours between fatal crashes.

Explain what we mean by saying a random variable is approximately normally distributed.

Your high school graduating class had 564 members.Thirty-three percent of these are expected to attend college.If the number of students who attend college follows the normal distribution,the probability that less than 160 will attend college is:

A statistics class is composed of 60 percent females.If 15 students are selected randomly,what is the probability that this group will include either 8,9,10,or 11 females? Use the normal distribution.

Let x be a binomial random variable.Find P(x ≥ 40)if n = 100 and $\pi$ = 0.32.

Under certain conditions,the normal distribution can be used to approximate the binomial distribution.

Which of the following is not true for an exponential distribution with parameter $\lambda$ ?

A manufacturer of tow chains finds that the average breaking point is at 3,500 pounds and the standard deviation is 250 pounds.If you pull a weight of at least 4200 pounds with this tow chain,what percentage of the time would you expect the chain to break?

There exists a different normal curve for every possible pair of $\mu$ and $\text { ?}$ .