Exam 6: Continuous Probability Distributions

Exhibit 6-5 The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes. -Refer to Exhibit 6-5. The probability that her trip will take longer than 60 minutes is

Given that Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.1401?

The Mathematics part of the SAT scores of students at UTC are normally distributed with a mean of 500 and a standard deviation of 75. a. If 2.28 percent of the students who had the highest scores received scholarships, what was the minimum score among those who received scholarships? Do not round your answer. b. It is known that 6.3 percent of students who applied to UTC were not accepted. What is the highest score of those who were denied acceptance? Do not round your answer. c. What percentage of students had scores between 575 and 650?

A negative value of Z indicates that

The exponential probability distribution is used with

The records show that 8% of the items produced by a machine do not meet the specifications. Use the normal approximation to the binomial distribution to answer the following questions. What is the probability that a sample of 100 units contains a. Five or more defective units? b. Ten or fewer defective units? c. Eleven or less defective units?

The time it takes a mechanic to change the oil in a car is exponentially distributed with a mean of 5 minutes. a. What is the probability density function for the time it takes to change the oil? b. What is the probability that it will take a mechanic less than 6 minutes to change the oil? c. What is the probability that it will take a mechanic between 3 and 5 minutes to change the oil? d. What is the variance of the time it takes to change the oil?

The weights of items produced by a company are normally distributed with a mean of 4.5 ounces and a standard deviation of 0.3 ounces. a. What is the probability that a randomly selected item from the production will weigh at least 4.14 ounces? b. What percentage of the items weigh between 4.8 to 5.04 ounces? c. Determine the minimum weight of the heaviest 5% of all items produced. d. If 27,875 of the items of the entire production weigh at least 5.01 ounces, how many items have been produced?

The time required to assemble a part of a machine follows an exponential probability distribution with a mean of 14 minutes. a. What is the probability that the part can be assembled in 7 minutes or less? b. What is the probability that the part can be assembled between 3.5 and 7 minutes?

Exhibit 6-8 The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. -Refer to Exhibit 6-8. What percentage of tires will have a life of 34,000 to 46,000 miles?

For a standard normal distribution, the probability of obtaining a z value between -1.9 to 1.7 is

Exhibit 6-10 A professor at a local university noted that the grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. -Refer to Exhibit 6-10. Students who made 57.93 or lower on the exam failed the course. What percent of students failed the course?

A professor at a local community college noted that the grades of his students were normally distributed with a mean of 74 and a standard deviation of 10. The professor has informed us that 6.3 percent of his students received A's while only 2.5 percent of his students failed the course and received F's. a. What is the minimum score needed to make an A? b. What is the maximum score among those who received an F? c. If there were 5 students who did not pass the course, how many students took the course?

The uniform, normal, and exponential distributions are

The average price of cell phones manufactured by Ahmadi, Inc. is $98 with a standard deviation of $12. Furthermore, it is known that the prices of the cell phones manufactured by Ahmadi are normally distributed. a. What percentage of cell phones produced by Ahmadi, Inc. will have prices of at least $120.20? b. Cell phones with prices of at least 81.80 will get a free gift. What percentage of the cell phones will be eligible for the free gift? c. What are the minimum and the maximum values of the middle 95% of cell phone prices? d. If 7,218 of the Ahmadi cell phones were priced at least $119.00, how many cell phones were produced by Ahmadi, Inc.?

A normal distribution with a mean of 0 and a standard deviation of 1 is called

Exhibit 6-4 fx) =1/10) e-x/10 x ≥ 0 -Refer to Exhibit 6-4. The probability that x is less than 5 is

The standard deviation of a standard normal distribution

The uniform probability distribution is used with

The center of a normal curve is