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Exam 6: Continuous Probability Distributions

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Question 61

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Exhibit 6-1 The assembly time for a product is uniformly distributed between 6 to 10 minutes. -Refer to Exhibit 6-1.The probability density function has what value in the interval between 6 and 10?

A) 0.25
B) 4.00
C) 5.00
D) zero

E) B) and C)
F) B) and D)

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Question 62

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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 of at least 26 is

A) 0.000
B) 0.125
C) 0.250
D) 1.000

E) A) and C)
F) A) and D)

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Question 63

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The average life expectancy of computers produced by Ahmadi,Inc.is 6 years with a standard deviation of 10 months.Assume that the lives of computers are normally distributed.Suggestion: For this problem,convert ALL of the units to months. a.What is the probability that a randomly selected computer will have a life expectancy of at least 7 years? b.Computers that fail in less than 5¹/₂ years will be replaced free of charge.What percentage of computers are expected to be replaced free of charge? c.What are the minimum and the maximum life expectancy of the middle 95% of the computers' lives? Give your answers in months and do not round your answers. d.The company is expecting that only 104 of this year's production will fail in less than 3 years and 8 months.How many computers were produced this year?

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 percent of players weigh between 180 and 220 pounds?

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?

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

Which of the following is not a characteristic of the normal probability distribution?

Larger values of the standard deviation result in a normal curve that 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

A standard normal distribution is a normal distribution

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?

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

For a uniform probability density function,

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.

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 ¹/₂ 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 time it takes to completely tune an engine of an automobile follows an exponential distribution with a mean of 40 minutes. a.What is the probability of tuning an engine in 30 minutes or less? b.What is the probability of tuning an engine between 30 and 35 minutes?

X is a normally distributed random variable with a mean of 22 and a standard deviation of 5.The probability that X is less than 9.7 is

If the mean of a normal distribution is negative,

A uniform probability distribution is a continuous probability distribution where the probability that the random variable assumes a value in any interval of equal length is

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?