SOLUTION: The population of weights of a particular fruit is normally distributed, with a mean of 328 grams and a standard deviation of 28 grams. If 8 fruits are picked at random, then 12% o
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Question 1196930: The population of weights of a particular fruit is normally distributed, with a mean of 328 grams and a standard deviation of 28 grams. If 8 fruits are picked at random, then 12% of the time, their mean weight will be greater than how many grams? Round your answer to the nearest gram.
You can put this solution on YOUR website! population mean = 328 grams
population standard deviation = 28 grams
sample size is 8 pieces of fruit
standard error = standard deviation / square root of sample size = 28 / sqrt(8) = 9.8995 rounded to 4 decimal places.
z-score = inverse(.88) = 1.175
88% of the sample means will be below that and 12% will be above that.
raw score = z * standard error + population mean = 1.175 * 9.8995 + 328 = 339.6319 rounded to 4 decimal places.
88% of the raw scores will be below that and 12% will be above that.
here's what it looks like on a z-score graphing calculator.
calculator can be found at https://davidmlane.com/hyperstat/z_table.htmlhttps://davidmlane.com/hyperstat/z_table.html
since you are dealing with the mean of the sample, you need the standard error and not the standard deviation.
