Question 1169482
mean = 238
standard deviation = 58
sample size = 49


standard error = standard deviation / square root of sample size.


standard error = 58/sqrt(49) = 58/7 = 8.285714286.


z-score = (x - m) / s


x is the raw score
m ie the mean
s is the standard error


z-score = (226 - 238) / 8.285714286 = -1.448275862


this can be rounded to -1.45 if you use the z-score tables.


it can be left as is if you use a calculator that can handle it.


i use the ti-84 plus which can handle it.


using the ti-84 plus, i get an area to the left of a z-score of -1.448275862 equal to .073769999.


that's the probability that the average of fly balls in the sample will be less than 226.


if use the z-score table, then the area to the left of a z-score of -1.45 is equal to .07353.


both results are acceptable.


the difference between .07353 and .073769999 is approximately 0.325% of .073769999.


that's well within the accuracy required.


here's what the result looks like using the online calculator that can be found at <a href = "https://www.calculator.net/z-score-calculator.html?c1raw=226&c1mean=238&c1sd=8.285714286&calctype=zscore&x=60&y=17" target = "_blank">https://www.calculator.net/z-score-calculator.html?c1raw=226&c1mean=238&c1sd=8.285714286&calctype=zscore&x=60&y=17</a>


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