Given a normally distributed population with a mean income of $40,000 and standard deviation of $7,500, what percentage of the population makes between $30,000 and $35,000? A) 13.34. B) 41.67. C) 31.92. D) 15.96.

are we allowed to use a z table? because if not, this seems impossible…

use a z table.

Is it D, 15.96?

yea, it’s D The z-score for $30,000 = ($30,000 – $40,000) / $7,500 or –1.3333, which corresponds with 0.0918. The z-score for $35,000 = ($35,000 – $40,000) / $7,500 or –0.6667, which corresponds with 0.2514. The difference is 0.1596 or 15.96%. I just took this question, and got it wrong because I haven’t done a question like it since september.

Ah ok… Finally it gives me some confidence. Been doing really badly in all my book 6 tests so far.

i’m presuming we don’t need to know how to reference z tables… right?

the reason i ask is, we’re not given z-tables in the exam… but yes, the answer is D. convert each point into a z-score… for 35(thousand): z1 = (35-40)/7.5 = -0.67 for 30: z2 = (30-40)/7.5 = -1.33 so, the area under z1, minus the area under z2, equals the range we’re looking for… so, 0.2514 - 0.0918 = 0.1596