The weights of ice cream cartons are normally distributed with a mean weight of 8 ounces and a standard deviation of 0.4 ounce. a) what is the probability that a randomly selected carton has a weight greater than 8.13 ounces? b) a sample of 16 cartons is randomly selected. what is the probability that their mean weight is greater than 8.13 ounces?

a) 0.373 probability that a randomly selected carton has a weight greater than 8.13 ounces

b) 0.097 probability that mean weight of 16 randomly selected carton is greater than 8.13 ounces

Step-by-step explanation:

We are given the following information in the question:

Mean, μ =  8 ounces

Standard Deviation, σ = 0.4 ounce

We are given that the distribution of weights of ice cream cartons is a bell shaped distribution that is a normal distribution.

Formula:

a) P(weight greater than 8.13 ounces)

P(x > 8.13)

Calculation the value from standard normal z table, we have,  

b) P(weight of 16 randomly selected cartons is greater than 8.13 ounces)

P(x > 8.13)

Calculation the value from standard normal z table, we have,  

answer: slight chance that it will happen

step-by-step explanation: