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 expected assembly time (in minutes) is

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

X is a normally distributed random variable with a mean of 5 and a variance of 4. The probability that X is greater than 10.52 is

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

The standard deviation of a standard normal distribution

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 weighs exactly 8 ounces?

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. What is the probability that a randomly selected computer will have a price of at least $1,530?

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

The probability that a continuous random variable takes any specific value

The ages of students at a university are normally distributed with a mean of 21. What percentage of the student body is at least 21 years old?

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.

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?

A normal probability distribution

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 at least 11.7 ounces?

A continuous random variable is uniformly distributed between a and b. The probability density function between a and b 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 0.9834?

For a standard normal distribution, the probability of obtaining a z value between -2.4 to -2.0 is

Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.9803?

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 between 11 and 12 ounces?

Approximate the following binomial probabilities by the use of normal approximation. a.P(X = 18, n = 50, p = 0.3) b.P(X 15, n = 50, p = 0.3) c.P(X 12, n = 50, p = 0.3) d.P(12 X 18, n = 50, p = 0.3)