SOLUTION: A manufacturer knows that their items have a lengths that are skewed right, with a mean of 13.5 inches, and standard deviation of 3.4 inches. If 46 items are chosen at random, w

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Question 1204602: A manufacturer knows that their items have a lengths that are skewed right, with a mean of 13.5 inches, and standard deviation of 3.4 inches.
If 46 items are chosen at random, what is the probability that their mean length is greater than 12.3 inches?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x̄ = 12.3+ => mean length
sample size n=++46

population mean mu=+13.5+
standard deviation sigma=+3.4

to find: P(x̄ > 12.3)

z-statistic: (x̄ -mu)/%28sigma%2Fsqrt%28n%29%29

compute z-statistic for x̄ = 12.3+

z+=+%2812.3+-+13.5%29%2F%283.4%2Fsqrt%2846%29%29+=+-2.393763523456

P%28z+%3E+-2.393763523456%29+=++0.99166175 =>99.166175% chance of the sample mean being greater than 12.3+inches long