Exam 6: Continuous Probability Distributions

The contents of soft drink bottles are normally distributed with a mean of twelve ounces and a standard deviation of one ounce. a. What is the probability that a randomly selected bottle will contain more than ten ounces of soft drink? b. What is the probability that a randomly selected bottle will contain between 9.5 and 11 ounces? c. What percentage of the bottles will contain less than 10.5 ounces of soft drink?

In grading eggs into small, medium, and large, the Nancy Farms packs the eggs that weigh more than 3.6 ounces in packages marked "large" and the eggs that weigh less than 2.4 ounces into packages marked "small"; the remainder are packed in packages marked "medium." If a day's packaging contained 10.2% large and 4.18% small eggs, determine the mean and the standard deviation for the eggs' weights. Assume that the distribution of the weights is normal.

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?

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 exactly 50 minutes is

The driving time for an individual from his home to his work is uniformly distributed between 300 to 480 seconds. a. Determine the probability density function. b. Compute the probability that the driving time will be less than or equal to 435 seconds. c. Determine the expected driving time. d. Compute the variance. e. Compute the standard deviation.

Z is a standard normal random variable. The P 1.41 ≤ Z ≤ 2.85) equals

An exponential probability distribution

Given that Z is a standard normal random variable, what is the probability that -2.51 ≤ Z ≤ -1.53?

A professor at a local university noted that the grades of her students were normally distributed with a mean of 78 and a standard deviation of 10. a. The professor has informed us that 16.6 percent of her students received grades of A. What is the minimum score needed to receive a grade of A? b. If 12.1 percent of her students failed the course and received F's, what was the maximum score among those who received an F? c. If 33 percent of the students received grades of B or better i.e., A's and B's), what is the minimum score of those who received a B?

The probability density function for a uniform distribution ranging between 2 and 6 is

For any continuous random variable, the probability that the random variable takes on exactly a specific value is

Z is a standard normal random variable. The P-1.96 ≤ Z ≤ -1.4) equals

For a uniform probability density function,

A value of 0.5 that is added and/or subtracted from a value of x when the continuous normal distribution is used to approximate the discrete binomial distribution is called

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

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?

The monthly income of residents of Daisy City is normally distributed with a mean of $3000 and a standard deviation of $500. a. The mayor of Daisy City makes $2,250 a month. What percentage of Daisy City's residents has incomes that are more than the mayor's? b. Individuals with incomes of less than $1,985 per month are exempt from city taxes. What percentage of residents is exempt from city taxes? c. What are the minimum and the maximum incomes of the middle 95% of the residents? d. Two hundred residents have incomes of at least $4,440 per month. What is the population of Daisy City?

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

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 $30,000?

Given that Z is a standard normal random variable. What is the value of Z if the area to the left of Z is 0.9382?