Click here to open the distribution applet When I was 16 1 drove a Dodge Colt. T

Question

Click here to open the distribution applet When I was 16 1 drove a Dodge Colt. The broken gas gauge always read empty, but I knew the distance it could go on a tank of gas is normally distributed with a mean of 340 miles and a standard deviation of 16 miles. a) What is the probability that the next tank will go for exactly 326 miles? Use 4 decimal places b) What is the probability that the next tank will go for less than 320.8 miles? Use 4 decimal places There's no way to guarantee I'll never run out of gas, but I want to make sure it only happens 4% of the time. How many miles do I dare drive before filling up again? Use 1 decimal place miles

Explanation / Answer

a) P( Exactly 326 miles ) = 0 ( because for continuous distributions the probability at exact value is 0)

b) P(X<320.8)

= P(Z<(320.8-340)/16)

= P(Z<-1.2)

= 0.1151

c) For top 4% Critical valuw would be 1.75

Miles = 1.75*16+340 = 368.0

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