Ice Cream The weights of ice cream cartons are normally distri...

Question

Ice Cream The weights of ice cream cartons are normally distributed with a mean weight of 10 ounces and a standard deviation of 0.5 ounce.

a. What is the probability that a randomly selected carton has a weight greater than 10.21 ounces?

Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says a nutrition company packages snack bars that have weights normally distributed around a mean of 15 g with a standard deviation of 0.4 g. Calculate the probability that a randomly chosen snack bar weighs more than 15.3 g. And we're given four possible choices as our answers. For choice A, we have 0.2266. For choice B, we have 0.2626. For choice C, we have 0.6622, and for choice D, we have 0.2426. So we're asked to calculate the probability that a randomly chosen snack bar weighs more than 15.3 g. So the first step is to convert our 15.3 g into a Z score. So here, we call your formula for a Z score, that is Z going to be equal to the quantity of X minusu in quantity divided by sigma. Where Z here is our Z score, X is going to be the weight of our stack bar, mu is going to be our mean, and sigma is our standard deviation. So we're given all those values in our problem here. That means Z is going to be equal to. For X, we have our 15.3 g. We'll have 15.3 minus u, which is our mean, which we're told is 15 g, so we'll have minus 15, and then that quantity is going to be divided by our standard deviation sigma, which we're told and the problem is 0.4 g. We'll divide this by 0.4. And so when we evaluate this expression, we get that Z is going to be equal to. 0.75. So, in order to find a probability, we need to find the area under our Normal distribution curve to the right of our Z score, because that will give us the probability of the snack bar weighing more than 15.3 g. So, using our standard normal distribution tables, we see that the cumulative probability, capital P, of Capital Z Less than or equal to 0.75. Is going to be equal to. 0.7734. However, this is the a cumulative probability, and so this is going to be the area to the left of our Z value of 0.75. But we're interested in the area to the right. So what we're actually looking for is the probability P of Z is greater than 0.75. And so here we just need to take the compliments. So this is going to be equal to 1 minus 0.7734. And when we evaluate the expression, that is going to be equal to. 0 point. 2266. So that is also going to be the probability. Of finding a snack bar that weighs more than 15.3 g. This is the answer that we're looking for for this problem. And so when we compare our answer here to our answer choices, we see that the correct answer choice corresponds to answer choice A. So I hope that this explanation has been useful, and I'll see you in the next video.

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Ice Cream The weights of ice cream cartons are normally distributed with a mean weight of 10 ounces and a standard deviation of 0.5 ounce.

a. What is the probability that a randomly selected carton has a weight greater than 10.21 ounces?

Key Concepts

Normal Distribution

Z-Score

Probability Calculation

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Ice Cream The weights of ice cream cartons are normally distributed with a mean weight of 10 ounces and a standard deviation of 0.5 ounce.a. What is the probability that a randomly selected carton has a weight greater than 10.21 ounces?