Due to COVID-19, a new hand sanitizer factory is now established in Tampa. Each bottle of hand sanitizer (150 grams) is intended to contain exactly

80% ethyl alcohol (120 grams). However, the manufacturing process is not perfect. Assume the error (in grams) of the amount of alcohol in a bottle

of hand sanitizer is a normal random variable with mean zero and standard deviation of 5 grams.

1. Let W denote the amount of alcohol contained in a bottle of hand sanitizer produced by the factory, and let denote the error the machine

makes. What is the PDF of W?

2. Let X=(/5)2. Compute the PDF of X; Specify the

range of values X can take.

3. Compute the moment generating function of X, Mx(t); Specify the range of values of t for which Mx(t) is finite.

4. Use your computed Mx(t) to compute the mean and variance of X.