SOLUTION: The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.54 inches and a standard deviation of 0.05 inch. A random sample of 10 tennis b
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Question 1204513: The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.54 inches and a standard deviation of 0.05 inch. A random sample of 10 tennis balls is selected. What is the probability that the sample mean is less than 2.53 inches? Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! population mean is 2.54
population standard deviation is .05
sample size is 10.
standard error is standard deviation / sqrt(sample size) = .0158114.
z = (x - m) / s
z is the z-score
x is the sample mean for test
m is the population mean
s is the standard error.
formula becomes z = (2.53 - 2.54) / .0158114 = - .632455.
area to the left of that z-score under the normal distribution curve is equal to .2635.
this means probability of the mean of a sample of 10 tennis balls having a diameter less than 2.53 is equal to 26.35%.
here's what it looks like on a normal distribution calculator.
