Packages of sugar bags for Sweeter Sugar Inc.have an average weight of 16 ounces and a standard deviation of 0.2 ounces.The weights of the sugar bags are normally distributed.What is the probability that 16 randomly selected packages will have a weight in excess of 16.075 ounces?
A).0500
B).3520
C).9332
D).0668

Question

Quizplus · Accepted Answer

We can use the formula for a z-score:
z-score = (x - μ) / σ

where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

In this case, we want to find the probability that the weight of 16 randomly selected packages will be greater than 16.075 ounces, so x = 16.075. The mean is μ = 16 and the standard deviation is σ = 0.2.

Plugging in the values, we get:

z-score = (16.075 - 16) / 0.2
z-score = 0.375

Using a standard normal distribution table or calculator, we can find that the area to the right of this z-score is 0.3520.

Therefore, the probability that 16 randomly selected packages will have a weight in excess of 16.075 ounces is 0.3520 or approximately 0.067 (rounded to three decimal places).

The closest choice is D, with a probability of 0.0668.

Packages of Sugar Bags for Sweeter Sugar Inc