Question

A racing car consumes a mean of 99 gallons of gas per race with a standard deviation of 3 gallons.

If 37 racing cars are randomly selected, what is the probability that the sample mean would be greater than 100.2 gallons? Round your answer to four decimal places.

Answer 1

Solution :

Given that ,

mean = = 99

standard deviation = = 3

n = 37

= 99 and

= / n = 3 / 37

P( > 100.2) = 1 - P( < 100.2)

= 1 - P(( - ) / < (100.2 - 99) / 3 / 37 )

= 1 - P(z < 2.4331)

= 1 - 0.9925 = 0.0075

P( > 100.2) = 0.0075

Probability = 0.0075