Answer:
a) 74.1331%
b) 0.7496%
c) 6.0472%
Explanation:
You want the percentages of graduates earning starting salaries in the given ranges, if starting salaries are normally distributed with a mean of $33440 and a standard deviation of $3930.
- $30,000–39,300
- > $43,000
- $39,300–43,000
Z-score
The z-score of the starting salaries is found by dividing the difference from the mean by the standard deviation. For example, the z-score of $30,000 is ...
(30,000 -33440)/3930 ≈ -0.88 . . . . . z-score for 30,000
Percentage
The fraction in a given range is the difference of CDF values for the z-scores at the ends of the range. The CDF values can be found from a table lookup or using a suitable calculator (see attached).
a) between $30,000 and 39,300 — 74.1331%
b) more than $43,000 — 0.7496%
c) between $39,300 and $43,000 — 6.0472%
__
Additional comment
The CDF values here are reported to 11 decimal places. We know that using -12 and +12 as representatives for -∞ and +∞ will not affect the CDF value in the first 11 decimal places, so that is why we use those values. (The calculator manual recommends ±1E999.)
In the normal course of computation, we only round numbers when they're reported at the end. There is nothing in the problem statement that requires reporting of z-scores, so we saw no need to round them. The final percentage values you get will be slightly different if you round the z-scores before using them in the CDF function.
<95141404393>