Question

The average cost of an IRS Form 1040 tax filing at Thetis Tax Service is $138.00. Assuming a normal distribution, if 77 percent of the filings cost less than $155.00, what is the standard deviation? Hint: Use Excel or Appendix C-2 to find the z-score. (Round your answer to 2 decimal places.) Standard deviation $

Answer 1

22.97

Explanation:

Given that the average cost of an IRS Form 1040 tax filing at Thetis Tax Service is $138.00.

Let x be the average cost an IRS Form 1040 tax filing at Thetis Tax Service

`P(X<155) = 0.77` is given

From std normal distribution table we find 77th percentile z value.

z=0.74

Corresponding X value = 155

i.e.
`0.74=(155-138)/(s)` where s is the std deviation

Simplify to get

Std deviation =
`(17)/(0.74) \\=22.97`