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,  

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.

the one below it is a function