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?

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

A local bank has determined that the daily balances of the checking accounts of its customers are normally distributed with an average of $280 and a standard deviation of $20. a.What percentage of its customers has daily balances of more than $275? b.What percentage of its customers has daily balances less than $243? c.What percentage of its customers' balances is between $241 and $301.60?

A uniform probability distribution is a continuous probability distribution where the probability that the random variable assumes a value in any interval of equal length is

If the mean of a normal distribution is negative,

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

Z is a standard normal random variable. The P (1.20 Z 1.85) equals

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 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 monthly earnings of computer systems analysts are normally distributed with a mean of $4,300. If only 1.07 percent of the systems analysts have a monthly income of more than $6,140, what is the value of the standard deviation of the monthly earnings of the computer systems analysts?

Exhibit 6-10 A professor at a local university noted that the exam grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. -Refer to Exhibit 6-10. The professor has informed us that 7.93 percent of her students received grades of A. What is the minimum score needed to receive a grade of A?

For a normal distribution, a negative value of z indicates

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?

The monthly earnings of computer programmers are normally distributed with a mean of $4,000. If only 1.7 percent of programmers have monthly incomes of less than $2,834, what is the value of the standard deviation of the monthly earnings of the computer programmers?

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?

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

X is a normally distributed random variable with a mean of 22 and a standard deviation of 5. The probability that X is less than 9.7 is

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 is the probability that a randomly selected tire will have a life of at least 47,500 miles?

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.?

In a standard normal distribution, the probability that Z is greater than zero is