Question

A racing car consumes a mean of 87 gallons of gas per race with a standard deviation of 6 gallons.

If 41 racing cars are randomly selected, what is the probability that the sample mean would differ from the population mean by less than 0.6 gallons? Round your answer to four decimal places.

Answer 1

Solution :

Given that,

mean = = 87

standard deviation = = 6

n = 41

= 87

= / n = 6 / 41

P(86.4 < < 87.6)

= P((86.4 - 87) / 6 / 41 <( - ) / < (87.6 - 87) / 6 / 41 ))

= P(-0.64 < Z < 0.64)

= P(Z < 0.64) - P(Z < -0.64) Using z table,

= 0.7389 - 0.2611

= 0.4778

Probability= 0.4778