Answer:
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 <em>A</em> = <em>X</em> + <em>X</em> and <em>B</em> = <em>A</em> - <em>Y</em>
The random variable <em>A</em> also follows a Normal distribution because the sum of two normal random variables is normal.
Similarly <em>B</em> also follows a normal distribution because the difference of two normal random variables is normal.
Compute the mean and variance of <em>A</em> as follows:
Compute the mean and variance of <em>B</em> 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.