Q5. According to the American Red Cross, 7% of people in the United States have blood type O-negative. A simple random sample of size 4 is obtained, and the number of people with blood type O-negative is recorded. Let X = the number of people with O-negative blood. A probability distribution for the random variable X as below:
X | P(X)
0 | 0.7481
1 | 0.2252
2 | 0.0254
3 | 0.0013
4 | 0
(a) Find the expected number of people with blood type O-negative for the sample using the general formula for expected value. (keep two decimals)
(b) Find the expected number of people with blood type O-negative for the sample using the "shortcut" method unique to the binomial distribution. (keep two decimals)
(c) Find the standard deviation. (keep two decimals)