Suppose that the weight of a gerbil is normally distributed with a mean of 12 ounces and a standard deviation of 3 ounces. What is the probability that a random sample of 10 gerbils has a sample mean of more than 14 ounces?
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µ = 12
σ = 3
x = 14
n = 10
z = (x - µ) /̘s
where s = σ/√n
z = (14 - 12) / (3/√10) = 2.1082
P(x < 14) = P( z =2.1082 ) = 0.982493
P( x > 14) 1 - P(x <14) = 0.0175
σ = 3
x = 14
n = 10
z = (x - µ) /̘s
where s = σ/√n
z = (14 - 12) / (3/√10) = 2.1082
P(x < 14) = P( z =2.1082 ) = 0.982493
P( x > 14) 1 - P(x <14) = 0.0175