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 more than 0.6 gallons? Would you be able to provide step by step instructions of how to get the answer in statcrunch?

Answer 1

Solution :

Given that,

mean = = 87

standard deviation = = 6

n = 41

= = 87

= / n = 6 / 41 = 0.94

87  ± 0.6 = 86.4, 87.6

P(86.4 < < 87.6)  

= P[(86.4 - 87) /0.94 < ( - ) / < (87.6 - 87) / 0.94)]

= P( -0.64 < Z < 0.64)

= P(Z < 0.64) - P(Z < -0.64)

Using z table,  

= 0.7389 - 0.2611

= 0.4778

P( x > 0.6 )

= 1 - P( x < 0.6 )

= 1 - 0.4778

= 0.5222