Question

1. 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. Assume that the variable is normally distributed

Answer 1

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