A college professor has found that the amount of gasoline he uses traveling from

Question

A college professor has found that the amount of gasoline he uses traveling from his luxurious Cary apartment to campus each week is normally distributed with a mean of 14.3 gallons and a standard deviation of 2.5 gallons.

For a randomly selected week, find the following to three decimal places. Probablities are values between 0 and 1.

Which sketch represents this probability? (place value in blank below picture)

 

b. Find the probability that the professor uses less than 16.5 gallons

Which sketch represents this probability? (place value in blank below picture)

 

 

c. Probability that the professor uses less than 11 gallons?

Which sketch represents this probability?

 

 

d. Find the probability that the professor uses between 16 and 18 gallons? _______?

e. Find the probability that the professor uses between 12 and 16 gallons?  ________?

f. What is the third quartile of the professor's gasoline usage?  _________?

 

 

A college professor has found that the amount of gasoline he uses traveling from his luxurious Cary apartment to campus each week is normally distributed with a mean of 14.3 gallons and a standard deviation of 2.5 gallons. For a randomly selected week, find the following to three decimal places. Probablities are values between 0 and 1. a. Find the probability that the professor uses over 17 gallons of gasoline. Which sketch represents this probability? (place value in blank below picture) probability = _____? b. Find the probability that the professor uses less than 16.5 gallons Which sketch represents this probability? (place value in blank below picture) probability = _______? c. Probability that the professor uses less than 11 gallons? Which sketch represents this probability? probability =________? d. Find the probability that the professor uses between 16 and 18 gallons? _______? e. Find the probability that the professor uses between 12 and 16 gallons? ________? f. What is the third quartile of the professor's gasoline usage? _________?

Explanation / Answer

Given X~Normal(=14.3, s=2.5)

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a. Find the probability that the professor uses over 17 gallons of gasoline.

P(X>17) = P((X-)/s >(17-14.3)/2.5)

=P(Z> 1.08)

= 0.140 (check standard normal table)

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b. Find the probability that the professor uses less than 16.5 gallons

P(X<16.5) = P(Z<(16.5-14.3)/2.5)

=P(Z<0.88)

= 0.8105(check standard normal table)

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c. Probability that the professor uses less than 11 gallons?

P(X<11) = P(Z<(11-14.3)/2.5)

=P(Z<-1.32)

=0.0934(check standard normal table)

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d. Find the probability that the professor uses between 16 and 18 gallons?

P(16<X<18) = P((16-14.3)/2.5 <Z< (18-14.3)/2.5)

=P( 0.68<Z<1.48)

= 0.1788(check standard normal table)

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e. Find the probability that the professor uses between 12 and 16 gallons?

P(12<X<16) = P((12-14.3)/2.5 <Z< (16-14.3)/2.5)

=P(-0.92<Z< 0.68)

= 0.5729 (check standard normal table)

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f. What is the third quartile of the professor's gasoline usage?

P(Z < (c-14.3)/2.5 )=0.75

--> (c-14.3)/2.5 =0.674 (check standard normal table)

--> c = 14.3 + 2.5*0.674 =15.985

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