Exam 6: Continuous Probability Distributions

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?

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 percentage of MBA's will have starting salaries of $34,000 to $46,000?

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 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 life expectancy of Timely brand watches is normally distributed with a mean of four years and a standard deviation of eight months. a. What is the probability that a randomly selected watch will be in working condition for more than five years? b. The company has a three-year warranty period on their watches. What percentage of their watches will be in operating condition after the warranty period? c. What is the minimum and the maximum life expectancy of the middle 95% of the watches? d. Ninety-five percent of the watches will have a life expectancy of at least how many months?

For a standard normal distribution, the probability of z ≤ 0 is

The time it takes a worker on an assembly line to complete a task is exponentially distributed with a mean of 8 minutes. a. What is the probability density function for the time it takes to complete the task? b. What is the probability that it will take a worker less than 4 minutes to complete the task? c. What is the probability that it will take a worker between 6 and 10 minutes to complete the task?

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.

The highest point of a normal curve occurs at

Exhibit 6-1 The assembly time for a product is uniformly distributed between 6 to 10 minutes. -Refer to Exhibit 6-1. The expected assembly time in minutes) is

Which of the following is not a characteristic of the normal probability distribution?

The salaries of the employees of a corporation are normally distributed with a mean of $25,000 and a standard deviation of $5,000. a. What is the probability that a randomly selected employee will have a starting salary of at least $31,000? b. What percentage of employees has salaries of less than $12,200? c. What are the minimum and the maximum salaries of the middle 95% of the employees? d. If sixty-eight of the employees have incomes of at least $35,600, how many individuals are employed in the corporation?

The weights of the contents of cans of tomato sauce produced by a company are normally distributed with a mean of 8 ounces and a standard deviation of 0.2 ounces. a. What percentage of all cans produced contain more than 8.4 ounces of tomato paste? b. What percentage of all cans produced contain less than 7.8 ounces? c. What percentage of cans contains between 7.4 and 8.2 ounces? d. Ninety-five percent of cans will contain at least how many ounces? e. What percentage of cans contains between 8.2 and 8.4 ounces?

The price of a bond is uniformly distributed between $80 and $85. a. What is the probability that the bond price will be at least $83? b. What is the probability that the bond price will be between $81 to $90? c. Determine the expected price of the bond. d. Compute the standard deviation for the bond price.

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 6-4 fx) =1/10) e-x/10 x ≥ 0 -Refer to Exhibit 6-4. The probability that x is between 3 and 6 is

For a standard normal distribution, the probability of obtaining a z value of less than 1.6 is

The Body Paint, an automobile body paint shop, has determined that the painting time of automobiles is uniformly distributed and that the required time ranges between 45 minutes to 1 hours. a. Give a mathematical expression for the probability density function. b. What is the probability that the painting time will be less than or equal to one hour? c. What is the probability that the painting time will be more than 50 minutes? d. Determine the expected painting time and its standard deviation.

Z is a standard normal random variable. The P-1.5 ≤ Z ≤ 1.09) equals