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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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