A market research team compiled the following discrete probability distribution for families residing in Pictou County. In this distribution, x represents the number of evenings the family dines outside their home during a week: The standard deviation of x is ___.
A) 1.00
B) 2.00
C) 0.80
D) 0.89
E) 1.09

Question

A market research team compiled the following discrete probability distribution for families residing in Pictou County. In this distribution, x represents the number of evenings the family dines outside their home during a week:  The standard deviation of x is ___.
A) 1.00 
B) 2.00 
C) 0.80 
D) 0.89 
E) 1.09

Quizplus · Accepted Answer

To find the standard deviation, we need to calculate the variance first. Using the formula for variance:

Var(X) = Σ [ xi - E(X) ]^2 * P(xi)

where E(X) is the expected value or mean of x, which is calculated as:

E(X) = Σ xi * P(xi)

By plugging in the values from the given table, we get:

E(X) = 2.8

To calculate the variance:

Var(X) = (0-2.8)^2 * 0.15 + (1-2.8)^2 * 0.25 + (2-2.8)^2 * 0.35 + (3-2.8)^2 * 0.25

Var(X) = 1.96

Finally, taking the square root of the variance, we get the standard deviation:

SD(X) = sqrt(Var(X)) = sqrt(1.96) = 0.89

Therefore, the answer is D) 0.89.

A Market Research Team Compiled the Following Discrete Probability Distribution