Suppose that the time required to complete a 1040R tax form is normally distributed with a mean of 90 minutes and a standard deviation of 10 minutes. What proportion of 1040R ta…

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asked Feb 11, 2023 166k views

1 Answer

Oae · Answer 1 · 2023-02-16T20:24:56+0000

Finding the proportion is the same as finding the following probability:

$P(X\ge77)$

in a normal distribution with mean 90 and standard deviation 10. To find this probability we use the z-score, defined by:

$Z=(x-\mu)/(\sigma)$

where x is the value we need (in this case x=77), hence the probability we are looking for can be calculated as:

$P(X\ge77)=P(Z\ge(77-90)/(10))=P(Z\ge-1.3)$

Using the tables of a normal distribution we have that:

$P(Z\ge-1.3)=0.9032$

Hence:

$P(X\ge77)=0.9032$

Therefore, 90.32% of tax forms will be completed in more than 77 minutes.