Question

# When conducting research on color blindness in​ males, a researcher forms random groups with five males...

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. 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.

x ​P(x) 0 0.662
1: 0.282
2: 0.052
3: 0.003
4: 0.001
5: 0.000

Does the table show a probability​ distribution? Select all that apply.

A. ​Yes, the table shows a probability distribution.

B. ​No, not every probability is between 0 and 1 inclusive.

C. ​No, the random variable​ x's number values are not associated with probabilities.

D. ​No, the random variable x is categorical instead of numerical.

E. ​No, the sum of all the probabilities is not equal to 1.

Find the mean of the random variable x. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A. "mue"= _____​male(s) ​(Round to one decimal place as​ needed.)
B. The table does not show a probability distribution.

Find the standard deviation of the random variable x. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A. "sigma" = _____ ​male(s) ​(Round to one decimal place as​ needed.)
B. The table does not show a probability distribution.

Solution :

 x P(x) x * P(x) x2 * P(x) 0 0.662 0 0 1 0.282 0.282 0.282 2 0.052 0.104 0.208 3 0.003 0.009 0.027 4 0.001 0.004 0.016 5 0 0 0 Sum 1 0.399 0.533

A. ​Yes, the table shows a probability distribution.

Mean = = X * P(X) = 0.399 = 0.4

Standard deviation =

=X 2 * P(X) - 2

=  [0.533 - 0.3992)

= 0.6

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