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Chapter 5: Q.5.5 (page 323)

Suppose the time it takes a student to finish a quiz is uniformly distributed between six and 15 minutes, inclusive. Let X=the time, in minutes, it takes a student to finish a quiz. Then X~U(6,15)Find the probability that a randomly selected student needs at least eight minutes to complete the quiz. Then find the probability that a different student needs at least eight minutes to finish the quiz given that she has already taken more than seven minutes.

Short Answer

Expert verified

The probability that a randomly selected student needs at least eight minutes to complete the quiz is 0.7778.

The probability that a different student needs at least eight minutes to finish the quiz given that she has already taken more than seven minutes is 0.875.

Step by step solution

01

Given Information

Given in the question that X~U(6,15)

Wherea=6andb=15

02

The probability density function 

The probability density function will be,

f(x)=1b鈭�a

=115鈭�6

=19

03

Calculate the value of P(x≥8)

The probability of student needs at least 8 minutes to complete the quiz can be computed as

P(x鈮�8)=basexheight

=(15鈭�8)19

=7脳19

=0.7778

04

Calculate the value of P(x>8∣x>7)

The probability of student needs at least 8 minutes to complete the quiz given 7 minutes that is P(x>8鈭�x>7)can be calculated as below:

The probability density function or height for this probability will be:

f(x)=1b鈭�a

=115鈭�7

=18

Therefore, the value of P(x>8鈭�x>7)is,

P(x>8鈭�x>7)=base脳height

=(15鈭�8)脳18

=7脳18

=0.875

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Most popular questions from this chapter

A subway train arrives every eight minutes during rush hour. We are interested in the length of time a commuter must wait for a train to arrive. The time follows a uniform distribution. a. Define the random variable. X = _______ b. X ~ _______ c. Graph the probability distribution. d. f(x) = _______ e. 渭 = _______ f. 蟽 = _______ g. Find the probability that the commuter waits less than one minute. h. Find the probability that the commuter waits between three and four minutes. i. Sixty percent of commuters wait more than how long for the train? State this in a probability question, similarly to parts g and h, draw the picture, and find the probabilit

Use the following information to answer the next eleven exercises. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years.

The distribution for Xis ______.

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a. Write the random variable X in words. X = __________________.

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