In: Statistics and Probability
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?
Solution :
Given that ,
mean = = 15
standard deviation = = 3.0
n = 30
= = 15
= / n = 3.0 / 30
P(14.5 < < 15.5)
= P[(14.5 - 15) / 3.0 / 30 < ( - ) / < (15.5 - 15) / 3.0 / 30)]
= P(-0.91 < Z < 0.91)
= P(Z < 0.91) - P(Z < -0.91)
Using z table,
= 0.8186 - 0.1814
= 0.6372