Question

The average clothes washer uses 15 gallons of water per load, with a standard deviation of 3.0 gallons. What is the probability that a random sample of 30 loads will provide a sample mean within one half gallon of the population mean?

Answer 1

Solution :

Given that,

mean = = 15 gallons

standard deviation = = 3.0 gallons

n = 30

= = 15 gallons

= / n = 3.0 / 30 = 0.55

15 ± 0.5 = 14.5, 15.5

P( 14.5 < < 15.5)  

= P[(14.5 - 15) /0.55 < ( - ) / < (15.5 - 15) / 0.55)]

= P( -0.91 < Z < 0.91)

= P(Z < 0.91 ) - P(Z < -0.91)

Using z table,  

= 0.8186 - 0.1814  

= 0.6372