Exam 6: Continuous Probability Distributions

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

The Globe Fishery packs shrimp that weigh more than 1.91 ounces each in packages marked" large" and shrimp that weigh less than 0.47 ounces each into packages marked "small"; the remainder are packed in "medium" size packages. If a day's catch showed that 19.77 percent of the shrimp were large and 6.06 percent were small, determine the mean and the standard deviation for the shrimp weights. Assume that the shrimps' weights are normally distributed.

The function that defines the probability distribution of a continuous random variable is a

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. Computers with prices of more than $1,750 receive a discount. What percentage of the computers will receive the discount?

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?

The average starting salary for this year's graduates at 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?

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

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 is the minimum weight of the middle 95% of the players?

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(Z > 2.11) equals

The mean of a standard normal probability distribution

The daily dinner bills in a local restaurant are normally distributed with a mean of $28 and a standard deviation of $6. a.What is the probability that a randomly selected bill will be at least $39.10? b.What percentage of the bills will be less than $16.90? c.What are the minimum and maximum of the middle 95% of the bills? d.If twelve of one day's bills had a value of at least $43.06, how many bills did the restaurant collect on that day?

A professor at a local community college noted that the grades of his students were normally distributed with a mean of 74 and a standard deviation of 10. The professor has informed us that 6.3 percent of his students received A's while only 2.5 percent of his students failed the course and received F's. a.What is the minimum score needed to make an A? b.What is the maximum score among those who received an F? c.If there were 5 students who did not pass the course, how many students took the course?

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

Given that Z is a standard normal random variable. What is the value of Z if the area between -Z and Z is 0.754?

Exhibit 6-4 f(x) =(1/10) e^-x/10 x 0 -Refer to Exhibit 6-4. The mean of x 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 probability that X will take on a value between 21 and 25 is

The life expectancy of computer terminals is normally distributed with a mean of 4 years and a standard deviation of 10 months. a.What is the probability that a randomly selected terminal will last more than 5 years? b.What percentage of terminals will last between 5 and 6 years? c.What percentage of terminals will last less than 4 years? d.What percentage of terminals will last between 2.5 and 4.5 years? e.If the manufacturer guarantees the terminals for 3 years (and will replace them if they malfunction), what percentage of terminals will be replaced?

A normal probability distribution

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 minimum value of the middle 95% of computer prices?