Answer:
Explanation:
Since the weights of ice cream cartons are normally distributed,
we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = weights of ice cream cartons.
µ = mean weight
σ = standard deviation
From the information given,
µ = 9 ounces
σ = 0.6 ounce
a) The probability that their mean weight is greater than 9.28 ounces is expressed as
P(x > 9.28) = 1 - P(x ≤ 9.28)
For x = 9.28,
z = (9.28 - 9)/0.6 = 0.47
Looking at the normal distribution table, the probability value corresponding to the z score is 0.68
P(x > 9.28) = 1 - 0.68 = 0.32
b) z = (x - µ)/σ/√n
Where
n represents the number of samples
n = 16
z = (9.28 - 9)/(0.6/√16)
z = 1.87
Probability value = 0.97
P(x > 9.28) = 1 - 0.97 = 0.03