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Statistics/ Probability

by Dar.F.
(Michigan)











































if mean time to take a test is 22.3 minutes with a standard deviation of 2.8 minutes what is the probability of person taking test being between 18 and 23.1 minutes?

Comments for Statistics/ Probability

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Jun 04, 2011
Statistics / Probability
by: Staff


The question:

by Dar.F.
(Michigan)


if mean time to take a test is 22.3 minutes with a standard deviation of 2.8 minutes what is the probability of person taking test being between 18 and 23.1 minutes?


The answer:

I am going to a z-table to obtain an exact answer.

For your problem:

Your mean is: 22.3 minutes

Your standard deviation is: 2.8 minutes

For your problem the interval is: 18 to 23.1 minutes.


That means the person taking the test will complete it between - 1.53571 and +0.285714 standard deviations from the mean of 22.3 minutes

----------------------------

Lower boundary
18 - 22.3 = - 4.3 minutes

-4.3/2.8 = - 1.53571 std deviations from (below) the mean

Upper boundary

23.1-22.3 = +0.8 minutes

0.8/2.8 = +0.285714 std deviations from (above) the mean
----------------------------

Computing the probability using a z table

I used the following z table

(1) Click the following link to VIEW the z table; or (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter:

Use the Backspace key to return to this page:

http://www.solving-math-problems.com/images/Statistics-Probability-z-table.png

from the z table

the lower boundary of - 1.54 standard deviations below the mean gives us a probability of 0.4382

the upper boundary of +0.29 standard deviations about the mean give us a probability of 0.1141

to find the final answer to your question, add these two values together:

0.4382 + 0.1141 = 0.5523

This means there is a 55.23% probability that a person will complete the test in 18 and 23.1 minutes.

The 55.23% probability is the area under the normal curve between - 1.54 and +0.29 standard deviations from the mean.

(1) Click the following link to VIEW the area under the normal curve; or (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter:

Use the Backspace key to return to this page:

http://www.solving-math-problems.com/images/Statistics-Probability-normal-probability.png

The final answer to your question is: 55.23%.


Thanks for writing.

Staff
www.solving-math-problems.com



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