Question

According to the Red Cross, 7% of people in the U.S. have blood type 0-negative. A simple random sample of size 4 is obtained, and the number of people with 0-negative blood is recorded. Construct a probability distribution for the random variable X. X = number of people with O-negative blood

n Probability

Answer 1

X Probability

0 0.81551

1 0.17484

2 0.00849

3 0.00016

4 0.00001

The probability distribution for the random variable X, representing the number of people with O-negative blood in a simple random sample of size 4, is constructed based on the given information that 7% of the U.S. population has blood type O-negative.

To create the distribution, the probabilities for each possible outcome are determined. Since the sample size is 4, the probabilities are calculated for X=0,1,2,3, and 4. The probabilities are obtained by using the binomial probability formula, which accounts for the probability of success (having O-negative blood) and the number of trials.

The resulting probability distribution is as follows:

X∣Probability

0∣0.81551

1∣0.17484

2∣0.00849

3∣0.00016

4∣0.00001

This distribution indicates the likelihood of observing each possible number of people with O-negative blood in the sample, providing a comprehensive view of the potential outcomes and their associated probabilities.