Question

Dylan Jones kept careful records of the fuel efficiency of his new car. After the first twelve times he filled up the tank, he found the mean was 26.1 miles per gallon (mpg) with a sample standard deviation of 1.0 mpg.

Compute the 98% confidence interval for his mpg.

How many times should he fill his gas tank to obtain a margin of error below 0.15 mpg?

Answer #1

Solution :

Given that,

Population standard deviation = = 1.0

Margin of error = E = 0.15

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

Z_{/2}
= Z_{0.01} = 2.326

sample size = n = (Z_{/2}*
/ E) ^{2}

n = (2.326* 1.0/ 0.15)^{2}

n = 240.46

**n = 241**

**241 times should he fill his gas tank to obtain a margin
of error below 0.15 mpg.**

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