Exam 6: Continuous Distributions

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If the number of parking spots at urban grocery stores is uniformly distributed over the interval 90 to 140,inclusively (90 \le x \le 140),then the standard deviation of this distribution is __________________.

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Employees arrive at a cafeteria according to a Poisson process at an average rate of 30 employees per hour.The probability that after one employee arrives,the next one will arrive at least 3 minutes later is _________.

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A recent market study has determined that the probability that a young adult will be willing to try a new online financial service that your company is offering is 50%.In a random sample of 10 young adults,the approximate probability that at least 2 but no more than 3 will be willing to try this new service is _________.

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The area under the standard normal distribution between -1 and 1 is twice the area between 0 and 1.

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If x,the time (in minutes)to complete an change job at certain auto service station,is uniformly distributed over the interval 20 to 30,inclusively (20 \le x \le 30),then the probability that an oil change job is completed in 21.75 to 24.25 minutes,inclusively,i.e.,P(21.75 \le x \le 24.25)is __________________.

(Multiple Choice)
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Participants in a 2 day biking event,cross the finish line at a rate of 10 bike riders per fifteen minute interval.The probability that at least 2 minutes will elapse between bike riders is _____________.

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Inquiries arrive at a record message device according to a Poisson process of rate 15 inquiries per minute.The probability that it takes more than 12 seconds for the first inquiry to arrive is approximately _________

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The expected (mean)life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours.The life of this bulb is normally distributed.What is the probability that a randomly selected bulb would last fewer than 1100 hours?

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Participants in a 2 day biking event,cross the finish line at a rate of 10 bike riders per fifteen minute interval.On average,how much time,in minutes,elapses between bike riders?

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If x is uniformly distributed over the interval 8 to 12,inclusively (8 \le x \le 12),then the probability,P(10.0 \le x \le 11.5),is __________________.

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If x,the time (in minutes)to complete an change job at certain auto service station,is uniformly distributed over the interval 20 to 30,inclusively (20 \le x \le 30),then the probability that an oil change job is completed in less than 17 minutes,i.e.,P(x < 17)is __________________.

(Multiple Choice)
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A standard normal distribution has a mean of one and a standard deviation of three.

(True/False)
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The expected (mean)life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours.The life of this bulb is normally distributed. What is the probability that a randomly selected bulb would last fewer than 940 hours?

(Multiple Choice)
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If x,the time (in minutes)to complete an oil change job at certain auto service station,is uniformly distributed over the interval 20 to 30,inclusively (20 \le x \le 30),then the standard deviation of this distribution is __________________.

(Multiple Choice)
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Since a normal distribution curve extends from minus infinity to plus infinity,the area under the curve is infinity.

(True/False)
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If the number of parking spots at urban grocery stores is uniformly distributed over the interval 90 to 140,inclusively (90 \le x \le 140),inclusively (90 \le x \le 140),then the mean of this distribution is __________________.

(Multiple Choice)
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A recent market study has determined that the probability that a young adult will be willing to try a new online financial service that your company is offering is 50%.In a random sample of 10 young adults,the probability that exactly 5 will be willing to try this new service is _________,and the approximate probability (using the normal distribution is)_________.

(Multiple Choice)
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The area under the standard normal distribution between 0 and 2 is twice the area between 0 and 1.

(True/False)
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At a certain workstation in an assembly line,the time required to assemble a component is exponentially distributed with a mean time of 10 minutes.Find the probability that a component is assembled in 7 minutes or less?

(Multiple Choice)
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Sure Stone Tire Company has established that the useful life of a particular brand of its automobile tires is normally distributed with a mean of 40,000 miles and a standard deviation of 5000 miles.What is the probability that a randomly selected tire of this brand has a life between 30,000 and 50,000 miles?

(Multiple Choice)
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