Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.
8. Male Color Blindness: When conducting research on color blindness in males, a researcher forms random groups with five males in each group. The random variable x is the number of males in the group who have a form of color blindness (based on data from the National Institutes of Health).
X P(x)
0 0.659
1 0.287
2 0.05
3 0.004
4 0.001
5 0+
p(x)-probability of x is missing
for standard deviation(sigma),we need mean (mu)
To determine whether a probability distribution is given, we can check if the sum of the probabilities is equal to 1.
In this case, let's add up the probabilities:
0.659 + 0.287 + 0.05 + 0.004 + 0.001 + 0 = 1.001
Since the sum of the probabilities is not exactly 1, there seems to be an error in the probability distribution. The probability for x = 5 is not given in the table.
To find the mean and standard deviation of a probability distribution, we need a valid probability distribution. However, since the probability for x = 5 is missing, we cannot proceed with finding the mean and standard deviation for this particular distribution.
In order to satisfy the requirements for a valid probability distribution, the sum of the probabilities should always equal 1.
To determine whether a probability distribution is given, we need to check if the probabilities listed in the table satisfy the requirements of a probability distribution:
1. The sum of all probabilities must equal 1.
2. All probabilities must be non-negative.
Let's check these requirements for the given probability distribution:
0.659 + 0.287 + 0.05 + 0.004 + 0.001 + 0 = 1
The sum of all probabilities is indeed equal to 1, which satisfies the first requirement.
Now, let's check if all the probabilities are non-negative:
0.659, 0.287, 0.05, 0.004, 0.001 are all non-negative probabilities.
However, we have encountered an issue with the last probability. It is listed as "0+," which may indicate that the probability is greater than zero but the actual value is not specified. This does not satisfy the requirement of having non-negative probabilities.
Therefore, the probability distribution is not given because the last probability is not provided. We cannot compute the mean and standard deviation without a complete probability distribution. To obtain a valid probability distribution, we need the value of the last probability, which is missing in this case.