Exam 6: Continuous Probability Distributions

The time it takes to hand carve a guitar neck is uniformly distributed between 110 and 190 minutes. a.What is the probability that a guitar neck can be carved between 95 and 165 minutes? b.What is the probability that the guitar neck can be carved between 120 and 200 minutes? c.Determine the expected completion time for carving the guitar neck. d.Compute the standard deviation.

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

For a continuous random variable x, the height of the function at x is

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 is the probability that a randomly selected item will weigh more than 10 ounces?

The highest point of a normal curve occurs at

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?

The miles-per-gallon obtained by the 1995 model Z cars is normally distributed with a mean of 22 miles-per-gallon and a standard deviation of 5 miles-per-gallon. a.What is the probability that a car will get between 13.35 and 35.1 miles-per-gallon? b.What is the probability that a car will get more than 29.6 miles-per-gallon? c.What is the probability that a car will get less than 21 miles-per-gallon? d.What is the probability that a car will get exactly 22 miles-per-gallon?

The ticket sales for events held at the new civic center are believed to be normally distributed with a mean of 12,000 and a standard deviation of 1,000. a.What is the probability of selling more than 10,000 tickets? b.What is the probability of selling between 9,500 and 11,000 tickets? c.What is the probability of selling more than 13,500 tickets?

The average starting salary of this year's graduates of a large university (LU) is $25,000 with a standard deviation of $5,000. 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 $31,000? b.Individuals with starting salaries of less than $12,200 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 68 of the recent graduates have salaries of at least $35,600, how many students graduated this year from this university?

Which of the following is a characteristic of the normal probability distribution?

Exhibit 6-1 The assembly time for a product is uniformly distributed between 6 to 10 minutes. -Refer to Exhibit 6-1. The probability of assembling the product in 7 minutes or more is

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 between 6.4 and 8.9 ounces?

Approximate the following binomial probabilities by the use of normal approximation. a.P(x < 12, n = 50, p = 0.3) b.P(12 < x < 18, n = 50, p = 0.3)

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. The probability of a player weighing more than 241.25 pounds is