1. In a lot of n components, 30% are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective,….

## Find the mean and standard deviation of the length of time that four bulbs will last.

1. If X and Y are independent random variables with means μX = 9.5 and μY = 6.8, and standard deviations σX = 0.4and σY = 0.1, find the means and standard deviations of the following:

a. 3X

b. Y − X

c. X + 4Y

2. The bottom of a cylindrical container has an area of 10 cm2 . The container is filled to a height whose mean is 5cm, and whose standard deviation is 0.1 cm. Let V denote the volume of fluid in the container.

a. Find μV .

b. Find σV .

3. The lifetime of a certain transistor in a certain application has mean 900 hours and standard deviation 30 hours. Find the mean and standard deviation of the length of time that four bulbs will last.