Please explain step by step if you can! The time required for a citizen to compl

Question

Please explain step by step if you can!
The time required for a citizen to complete the 2000 U.S. Census "long" form is normally distributed with a mean of 40 minutes and a standard deviation of 10 minutes. What proportion of the citizens will require less than one hour? time required for a citizen to complete the 2000 U.S. Census "long" form is normally distributed with a mean of 4 0 minutes and a standard deviation of 10 minutes. The slowest 10% of the citizens would need how many minutes to complete the form? 3. The time required for a citizen to complete the 2000 U.S. Census "long" form is normally distributed with a mean of 40 minutes and a standard deviation of 10 minutes. What is the third quartile (in minutes) for the time required to complete the form?

Explanation / Answer

1.) mu= 40,

sd=10

P(Xbar<60min)

Z= (Xbar-mu)/sd

=(60-40)/10 =2

Looking for the z table at z=2 for p value we get area under the curve as 0.9772499 and hence

We can say that P(Xbar>1hr) = 0.9772499

Ans = 0.9772499

2.) To find the slowest 10% we need to look for the z value at area of 90%

From Z table we get z value =1.281552 for area =0.9

Using the same formula used above

Z= (Xbar-mu)/sd

1.281552 = (Xbar-40)/10

Xbar=52.81552mins

So we conclude that the slowest 10% would require 52.81552 minuites

Ans = 52.81552minuites

3.) third quartile is from 50% till 75%

So solving the same for p=0.5 and p=0.75 we get z values as 0 and 0.6744898 respectively

Now solving the equation

Z= (Xbar-mu)/sd

0=(Xbar-40)/10

Xbar=40

&

Z= (Xbar-mu)/sd

0.6744898 = (Xbar-40)/10

Xbar=46.7449

Ans= Hence we conclude that the third quartile range is from 40 to 46.7449

Hope the above ans has helped you in understanding the problem. Pls upvote if it has really helped you. Good Luck!!

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