Exam 6: Continuous Probability Distributions

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 less than 6 minutes is

The mean of a standard normal probability distribution

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 is the minimum weight of the middle 95% of the players?

When a continuous probability distribution is used to approximate a discrete probability distribution

The average starting salary of this year's graduates of 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?

The salaries at a corporation are normally distributed with an average salary of $19,000 and a standard deviation of $4,000. a.What is the probability that an employee will have a salary between $12,520 and $13,480? b.What is the probability that an employee will have a salary more than $11,880? c.What is the probability that an employee will have a salary less than $28,440?

Given that Z is a standard normal random variable, what is the value of Z if the area to the right of Z is 0.5?

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?

The weekly earnings of bus drivers are normally distributed with a mean of $395. If only 1.1 percent of the bus drivers have a weekly income of more than $429.35, what is the value of the standard deviation of the weekly earnings of the bus drivers?

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 less than 250 pounds is

The length of time patients must wait to see a doctor in a local clinic is uniformly distributed between 15 minutes and 2 1/2 hours. a.What is the probability of a patient waiting exactly 50 minutes? b.What is the probability that a patient would have to wait between 45 minutes and 2 hours? c.Compute the probability that a patient would have to wait over 2 hours. d.Determine the expected waiting time and its standard deviation.

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 6-10 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. If 69.5 percent of the students received grades of C or better, what is the minimum score of those who received C's?

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

X is a normally distributed random variable with a mean of 12 and a standard deviation of 3. The probability that X equals 19.62 is

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 probability that X will take on a value between 21 and 25 is

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?

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?

Exhibit 6-6 The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. -Refer to Exhibit 6-6. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $47,500?

Exhibit 6-9 The average price of personal computers manufactured by MNM Company is $1,200 with a standard deviation of $220. Furthermore, it is known that the computer prices manufactured by MNM are normally distributed. -Refer to Exhibit 6-9. Computers with prices of more than $1,750 receive a discount. What percentage of the computers will receive the discount?