The average person uses 123 gallons of water daily. If the standard deviation is 21 gallons, find the probability that the mean usage of water of a randomly selected sample of 15 people will be greater than 126 gallons.
Solution :
Given that,
mean = = 123
standard deviation = = 21
n=15
= =123
= / n = 21 / 15 =5.42
P( > 126 ) = 1 - P( <126 )
= 1 - P[( - ) / < (126-123) /5.42 ]
= 1 - P(z < 0.55)
Using z table
= 1 - 0.7088
probability=0.2912
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