Suppose the following are the city driving gas mileages of a selection of sport

Question

Suppose the following are the city driving gas mileages of a selection of sport utility vehicles (SUVs). 19, 20, 19, 20, 18, 21, 17, 19, 24, 23, 21, 21, 17, 20, 20, 18 (a) Find the sample standard deviation (rounded to two decimal places). 1.94 (b) In what gas mileage range does Chebyshev's inequality predict that at least 75% of the selection will fall? (Enter your answer using interval notation. Round your answers to two decimal places.) [, ] (c) What is the actual percentage of SUV models of the sample that fall in the range predicted in part (b)? %

Explanation / Answer

b) As per Chebyshev's inequality, at least 75% of the selection will fall within 2 standard deviation from the mean.

Here,

Mean = 19.81

SD = 1.94

Hence,

Required interval will be:

(19.81 - 2(1.94), 19.81 + 2(1.94))

(15.93, 23.69)

c) Data values between 15.9 and 23.7 = 15

Total data = 16

So,

Actual percentage = 15/16 = 93.75%

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