The weights of ice cream cartons are normally distributed with a mean weight of 9 ounces and a standard deviation of 0.6 ounce. (a) What is the probability that a randomly selected carton has a weight greater than 9.28 ounces? (b) A sample of 16 cartons is randomly selected. What is the probability that their mean weight is greater than 9.28 ounces?

Step-by-step 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