Exam 6: Continuous Probability Distributions

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

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. Students who made 57.93 or lower on the exam failed the course. What percent of students failed the course?

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

Z is a standard normal random variable. The P (-1.20 Z 1.50) equals

Consider a binomial probability experiment with n = 3 and p = 0.1. Then, the probability of x = 0 is

A manufacturing process produces items whose weights are normally distributed. It is known that 22.57% of all the items produced weigh between 100 grams up to the mean and 49.18% weigh from the mean up to 190 grams. Determine the mean and the standard deviation.

Given that Z is a standard normal random variable, what is the probability that -2.08 Z 1.46?

A major department store has determined that its customers charge an average of $500 per month, with a standard deviation of $80. Assume the amounts of charges are normally distributed. a.What percentage of customers charges more than $380 per month? b.What percentage of customers charges less than $340 per month? c.What percentage of customers charges between $644 and $700 per month?

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?

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 z score for the standard normal distribution

The standard deviation of a normal distribution

A continuous random variable may assume

The random variable x is known to be uniformly distributed between 70 and 90. The probability of x having a value between 80 to 95 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 mean of X is

"DRUGS R US" is a large manufacturer of various kinds of liquid vitamins. The quality control department has noted that the bottles of vitamins marked 6 ounces vary in content with a standard deviation of 0.3 ounces. Assume the contents of the bottles are normally distributed. a.What percentage of all bottles produced contains more than 6.51 ounces of vitamins? b.What percentage of all bottles produced contains less than 5.415 ounces? c.What percentage of bottles produced contains between 5.46 to 6.495 ounces? d.Ninety-five percent of the bottles will contain at least how many ounces? e.What percentage of the bottles contains between 6.3 and 6.6 ounces?

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?

In a normal distribution, it is known that 27.34% of all the items are included from 100 up to the mean, and another 45.99% of all the items are included from the mean up to 145. Determine the mean and the standard deviation of the distribution.

In a standard normal distribution, the range of values of z is from

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 density function has what value in the interval between 20 and 28?