Question

A breakfast cereal producer makes its most popular product by combining just raisins and flakes in each box of cereal. The amounts of flakes in the boxes of this cereal are normally distributed with a mean of 370g and a standard deviation of 24g. The amounts of raisins are also normally distributed with a mean of 170g and a standard deviation of 7g. Let t= the total amount of product in a randomly selected box, and assume that the amounts of flakes and raisins are independent of each other. Find the probability that the total amount of product exceeds 515g. A) 0.0172 B) 0.0239 C) 0.0316 D) 0.0427

Answer 1

The probability that the total amount of product exceeds 515g is approximately A) 0.0172.

Step-by-step explanation:

To find the probability that the total amount of product exceeds 515g, we need to calculate the mean and standard deviation of the total amount of product, which is the sum of the amounts of flakes and raisins.

Since the amounts of flakes and raisins are independent, we can use the properties of normal distributions to find the mean and standard deviation of the total amount of product.

The mean of the total amount of product is the sum of the means of the amounts of flakes and raisins, which is 370g + 170g = 540g.

The standard deviation of the total amount of product is the square root of the sum of the variances of the amounts of flakes and raisins, which is sqrt(24^2 + 7^2) = sqrt(625) = 25g.

Now, we can standardize the total amount of product using the formula z = (x - mean) / standard deviation

Where

z is the standard score

x is the value

mean is the mean

standard deviation is the standard deviation.

In this case, we want to find the probability that the total amount of product exceeds 515g, which can be written as P(t > 515), where t is the total amount of product.

To find this probability, we can convert it to a standard score:

z = (515 - 540) / 25

Once we have the standard score, we can use the standard normal distribution table or a calculator to find the probability associated with it. In this case, the probability is approximately 0.0172.

Therefore, the correct answer is A) 0.0172.