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Assume a normal approximation to the binomial distribution.
Find mean and standard deviation.
mean = np
standard deviation = √npq
n = sample size
p = proportion
q = 1 - p
For your data:
n = 5
p = 1/7 (convert to a decimal for calculation purposes)
q = 1 - p
Once you determine the mean and standard deviation, use z-scores.
Formula:
z = (x - mean)/sd
x = 2.80
Finish the z-score calculation. Find the proportion of individual readings exceeding 2.80 grams by using a z-table.
I hope this will help get you started.