1. Consider a population with a bell-shaped distribution with a mean of 300 and standard deviation of 30.

a.Draw the distribution on the curve below including values in the scale for one, two, and three standard deviations from the mean.

b.Compute the z-scores for the following values of X and locate each on the graph.

X

Z-score

200

360

220

270

300

c.According to the Empirical rule what percent of the data should be between 270 and 330? Between 240 and 360?

d.According to Chebyshev what percent should be between 240 and 360?

e.Why is the z-score of the mean zero?

F. A student scores 33 on an English test that has a mean of 28 and a standard deviation of 5.He scores a 27 on a math test that has a mean of 25 and a standard deviation of 2.Which score is higher and why?