Question 1204513
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.
<img src = "http://theo.x10hosting.com/2023/102501.jpg">