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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 $

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Answer:

22.97

Step-by-step 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

[tex]P(X<155) = 0.77[/tex] is given

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

z=0.74

Corresponding X value = 155

i.e. [tex]0.74=\frac{155-138}{s}[/tex] where s is the std deviation

Simplify to get

Std deviation  = [tex]\frac{17}{0.74} \\=22.97[/tex]

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