Question

A sociologist randomly selects single adults for different groups of three and the random variable x is the number in the group who say that the most fun way to flirt is in person. 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 xP(x) 0 0.087 1 0.335 20.427 30.151 Does the table show a probability distribution? Select all that apply A. Yes, the table shows a probability distribution B. No, the sum of all the probabilities is not equal to 1. C. No, the random variable x is categorical instead of numerical D. No, not every probability is between 0 and 1 inclusive E. No, the random variable x's number values are not associated with probabilities 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 OA. adult(s) (Round to one decimal place as needed.) O 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 ơ- adult(s) (Round to one decimal place as needed.) O B. The table does not show a probability distribution Click to select and enter your answer(s)

Answer 1

the probability distribution is valid if the probability adds up to 1.

$0.087+0.335+0.427+0.151=1$

hence option A is right.

The mean of the random variable X

$\mu =\sum x_iP(x_i)=0(0.087)+1(0.335)+2(0.4277)+3(0.151)\approx 1.6$

standard deviation :

$\sigma =\sqrt{\sum x^2_iP(x_i)-\mu ^2}$

$\sum x^2_iP(x_i)=0(0.087)+1^2(0.335)+2^2(0.4277)+3^2(0.151)\approx 3.4$

$\sigma^2 =3.4-(1.6)^2=0.84$

$\sigma =\sqrt{\sum x^2_iP(x_i)-\mu ^2}=\sqrt{0.84}=0.9$ adults