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.