The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound-shaped and symmetric with a mean of 24.6 mpg and a standard deviation of 11.2 mpg. if 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 27

Question

Mathematics

Elian Noble

13 March, 02:43

The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound-shaped and symmetric with a mean of 24.6 mpg and a standard deviation of 11.2 mpg. if 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 27

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Adriel Brown · Answer 1

Mean (μ) = 24.6 mpg, Standard deviation (S. D) = 11.2 mpg and Sample size (n) = 30, Average greater than 27

z (27) = (27 - μ) / (S. D/sqrt n)

z (27) = 27 - 24.6 / (11.2/sqrt30)

z (27) = 1.17

P (x-bar >27) = P (z> 1.17) = normal cdf (1.17, 100) = 0.4152