Exam 6: Continuous Probability Distributions

The time it takes to completely tune an engine of an automobile follows an exponential distribution with a mean of 40 minutes. a. What is the probability of tuning an engine in 30 minutes or less? b. What is the probability of tuning an engine between 30 and 35 minutes?

Exhibit 6-2 The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. -Refer to Exhibit 6-2. What percent of players weigh between 180 and 220 pounds?

The length of time it takes students to complete a statistics examination is uniformly distributed and varies between 40 and 60 minutes. a. Find the mathematical expression for the probability density function. b. Compute the probability that a student will take between 45 and 50 minutes to complete the examination. c. Compute the probability that a student will take no more than 40 minutes to complete the examination. d. What is the expected amount of time it takes a student to complete the examination? e. What is the variance for the amount of time it takes a student to complete the examination?

Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.1112?

Exhibit 6-7 The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces. -Refer to Exhibit 6-7. What percentage of items will weigh at least 11.7 ounces?

The SAT scores of students are normally distributed with a mean of 950 and a standard deviation of 200. a. Nancy Bright's SAT score was 1390. What percentage of students have scores more than Nancy Bright? b. What percentage of students score between 1100 and 1200? c. What are the minimum and the maximum values of the middle 87.4% of the scores? d. There were 165 students who scored above 1432. How many students took the SAT?

The advertised weight on a can of soup is 10 ounces. The actual weight in the cans follows a uniform distribution and varies between 9.3 and 10.3 ounces. a. Give the mathematical expression for the probability density function. b. What is the probability that a can of soup will have between 9.4 and 10.3 ounces? c. What is the mean weight of a can of soup? d. What is the standard deviation of the weight?

Z is a standard normal random variable. The P -1.20 ≤ Z ≤ 1.50) equals

For a standard normal distribution, the probability of obtaining a z value between -2.4 to -2.0 is

The prices of condos in a city are normally distributed with a mean of $90,000 and a standard deviation of $28,000. a. The city government exempts the cheapest 6.68% of the condos from city taxes. What is the maximum price of the condos that will be exempt from city taxes? b. If 1.79% of the most expensive condos are subject to a luxury tax, what is the minimum price of condos that will be subject to the luxury tax?

The time between arrivals of customers at the drive-up window of a bank follows an exponential probability distribution with a mean of 10 minutes. a. What is the probability that the arrival time between customers will be 7 minutes or less? b. What is the probability that the arrival time between customers will be between 3 and 7 minutes?

The price of a stock is uniformly distributed between $30 and $40. a. What is the probability that the stock price will be more than $37? b. What is the probability that the stock price will be less than or equal to $32? c. What is the probability that the stock price will be between $34 and $38? d. Determine the expected price of the stock. e. Determine the standard deviation for the stock price.

The entire area under the standard normal distribution curve

The average starting salary for this year's graduates at a large university LU) is $20,000 with a standard deviation of $8,000. Furthermore, it is known that the starting salaries are normally distributed. a. What is the probability that a randomly selected LU graduate will have a starting salary of at least $30,400? b. Individuals with starting salaries of less than $15,600 receive a low income tax break. What percentage of the graduates will receive the tax break? c. What are the minimum and the maximum starting salaries of the middle 95% of the LU graduates? d. If 189 of the recent graduates have salaries of at least $32,240, how many students graduated this year from this university?

Scores on a recent national statistics exam were normally distributed with a mean of 80 and a standard deviation of 6. a. What is the probability that a randomly selected exam will have a score of at least 71? b. What percentage of exams will have scores between 89 and 92? c. If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award? d. If there were 334 exams with scores of at least 89, how many students took the exam?

A continuous probability distribution that is useful in describing the time, or space, between occurrences of an event is an)

Larger values of the standard deviation result in a normal curve that is

The ages of students at a university are normally distributed with a mean of 21. What percentage of the student body is at least 21 years old?

Approximate the following binomial probabilities by the use of normal approximation. a. Px ≤ 12, n = 50, p = 0.3) b. P12 ≤ x ≤ 18, n = 50, p = 0.3)

Exhibit 6-3 Consider the continuous random variable X, which has a uniform distribution over the interval from 20 to 28. -Refer to Exhibit 6-3. The variance of X is approximately