You're looking for the 15th percentile of a normal distribution with <em>µ</em> = 242 and <em>σ</em> = 13, which is to say you want to find <em>x</em> * such that
P(<em>X</em> ≤ <em>x</em> *) = 0.15
Transform the wait-time random variable <em>X</em> to <em>Z</em>, which follows the standard normal distribution with mean 0 and s.d. 1 :
<em>Z</em> = (<em>X</em> - <em>µ</em>) / <em>σ</em> → <em>X</em> = <em>µ</em> + <em>σ</em> <em>Z</em> = 242 + 13 <em>Z</em>
Now,
P(<em>X</em> ≤ <em>x</em> *) = P(242 + 13<em> Z</em> ≤ <em>x</em> *) = P(<em>Z</em> ≤ (<em>x</em> * - 242)/13) = 0.15
Use a calculator (something with an inverse CDF function) or <em>Z</em>-table to look up the <em>z</em>-score, <em>z</em> = (<em>x</em> * - 242)/13, associated with a probability of 0.15. You would find that
<em>z</em> = (<em>x</em> * - 242)/13 ≈ -1.03643
Solve for <em>x</em> * :
<em>x</em> * ≈ 242 + 13 (-1.03643) ≈ 228.526 ≈ 229
No answer choices provided but it’s because income is how much you are making before tax. Also, wealth means an abundance of currency so unless you are making lots of money, you dont have wealth. Hope this helps.
American ———————-/////————————
During the of condensation , water in a gas state changes to a liquid state.
$8.25
We can use a proportion.
6/5.5=9/x
Cross multiply: 6x=9(5.5)
6x=49.5
X=$8.25