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Exam 6: Continuous Probability Distributions

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Question 51

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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?

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a.87.7
b.6...

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Question 52

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The life expectancy of Timely brand watches is normally distributed with a mean of four years and a standard deviation of eight months. a.What is the probability that a randomly selected watch will be in working condition for more than five years? b.The company has a three-year warranty period on their watches.What percentage of their watches will be in operating condition after the warranty period? c.What is the minimum and the maximum life expectancy of the middle 95% of the watches? d.Ninety-five percent of the watches will have a life expectancy of at least how many months?

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a.0.0668
b.93.32%
c....

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Question 53

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

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

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

A continuous probability distribution that is useful in describing the time,or space,between occurrences of an event is a(n)

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 she will finish her trip in 80 minutes or less is

For a continuous random variable x,the probability density function f(x) represents

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?

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

The standard deviation of a standard normal distribution

Z is a standard normal random variable.The P(Z > 2.11) equals

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

Approximate the following binomial probabilities by the use of normal approximation.Twenty percent of students who finish high school do not go to college.What is the probability that in a sample of 80 high school students a.exactly 10 will not go to college? b.70 or more will go to college? c.fourteen or fewer will not go to college?

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?

Z is a standard normal random variable.The P (1.41 < Z < 2.85) 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?

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?

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?

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