Your local grocery store sells 5 lb bags of potatoes. However, the 5 lb bags do not weight exactly 5 lbs. If we let Xi be the weight of a randomly selected 5 lb bag of potatoes, historical data indicates that Xi ~ N(5.36, 0.14). The local warehouse store sells 10 lb bags of potatoes, which also do not weight exactly 10 lbs. If Y is the weight of a randomly selected 10 lb bag, historical data indicates that Y ~ N(10.22, 0.18). We randomly select two 5 lb bags of potatoes and one 10 lb bag of potatoes. What is the probability that the sum of the weights of the two 5 lb bags exceeds the weight of one 10 lb bag?

The probability that  the sum of the weights of the two 5 lb bags exceeds the weight of one 10 lb bag is 0.719.

Step-by-step explanation:

The random variable denote the weight of a 5 lb bag.

The random variable denote the weight of a 10 lb bag.

It is provided that:

Let A = X + X and B = A - Y

The random variable A also follows a Normal distribution because the sum of two normal random variables is normal.

Similarly B also follows a normal distribution because the difference of two normal random variables is normal.

Compute the mean and variance of A as follows:

Compute the mean and variance of B as follows:

Compute the probability that  the sum of the weights of the two 5 lb bags exceeds the weight of one 10 lb bag, i.e. P (A > Y)

**Use the standard normal table for the probability value.

Thus, the probability that  the sum of the weights of the two 5 lb bags exceeds the weight of one 10 lb bag is 0.719.

yes because there is exactly one y value for every x value

for function there can't be more than one value for every x value