Question

In your bid to be elected class representative, you have your election committee survey five randomly chosen students in your class and ask them to rank you on a scale of 0-10. Your rankings are 1, 2, 4, 0, 8. (a) Find the sample mean and standard deviation. (Round your answers to two decimal places.) HINT [See Example 1.] sample mean standard deviation (b) Assuming the sample mean and the standard deviation is indicative of the class as a whole, in what range does the empirical rule predict that approximately 68% of the class will rank you? , What other assumptions must we make to use the rule? The population distribution is bell-shaped, but not symmetric. The population distribution is symmetric, but not bell-shaped. The population distribution is neither bell-shaped nor symmetric. The population distribution is bell-shaped and symmetric.

Answer 1

$\dpi{120} \bar x$ = (1 + 2 + 4 + 0 + 8)/5 = 3

s = sqrt(((1 - 3)^2 + (2 - 3)^2 + (4 - 3)^2 + (0 - 3)^2 + (8 - 3)^2)/4) = 3.16

b) According to the empirical rule about 68% of the data fall within one standard deviation from the mean.

3 - 3.16 = -0.16

3 + 3.16 = 6.16

So the range is from -0.16 to 6.16.

The population distribution is bell-shaped and symmetric.