# What’s the mean and standard deviation?

The answer are 39.5 and 5.33

Thanks Relevance

Find the z-scores

(35 - m) / s = z

P(z) = 0.2

http://www.z-table.com/

z = -0.805 is a pretty good guess there

(35 - m) / s = -0.805

35 - m = -0.805 * s

35 = m - 0.805 * s

(45 - m) / s = z[b]

(35 - m) / s = -0.805 = z[a]

z[b] - z[a] = 0.65

z[b] - 0.2 = 0.65

z[b] = 0.85

z[b] =>> 1.035

45 - m = 1.035 * s

45 = m + 1.035 * s

35 = m - 0.805 * s

45 = m + 1.035 * s

45 - 35 = m + 1.035 * s - m + 0.805 * s

10 = 1.84 * s

10/1.84 = s

1000 / 184 = s

125 / 23 = s

s = 5.(4347826086956521739130)....

45 - 1.035 * s = m

m = 39.375

My answers are a little off from the key because I guessed on the z-scores.  With a numerical solver, you can get much closer results.

• The (arithmetic) mean is same as the average. Standard deviation is a measure of how spread out the values are for the whole population, thus is has units of whatever is being measured. A quick rule is that 95% of the population falls within 3 standard deviations either side of the mean.