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?

Answer:a) 0.373 probability that a randomly selected carton has a weight greater than 8.13 ouncesb) 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 ounceWe are given that the distribution of weights of ice cream cartons is a bell shaped distribution that is a normal distribution. Formula: [tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex] a) P(weight greater than 8.13 ounces) P(x > 8.13) [tex]P( x > 8.13) = P( z > \displaystyle\frac{8.13 - 8}{0.4}) = P(z > 0.325)[/tex] [tex]= 1 - P(z \leq 0.325)[/tex] Calculation the value from standard normal z table, we have,  [tex]P(x > 610) = 1 - 0.627 = 0.373 = 37.3\%[/tex]b) P(weight of 16 randomly selected cartons is greater than 8.13 ounces) P(x > 8.13) [tex]P( x > 8.13) = P( z > \displaystyle\frac{8.13 - 8}{\frac{0.4}{\sqrt{16}}}) = P(z > 1.3)[/tex] [tex]= 1 - P(z \leq 1.3)[/tex] Calculation the value from standard normal z table, we have,  [tex]P(x > 8.13) = 1 - 0.903 = 0.097 = 9.7\%[/tex]