# Continuous Random Variables and Prob. Distribution

Man I hate probability...anyhow could some help me with this Q as I am not understanding how to set it up...

Suppose that the force acting on a column which helps to support a building is normally distributed with mean 15.0 kips and standard deviation 1.25 kips:

What is the probability that the force differs from 15.0 kips by at most two standard deviations?

Do they mean this inequality:

12.5<F<17.5, where the < means greater than or equal to and > less than equal to

It just came to me by the way

Oh i know i am suppose to standardize the raw variable I jus didnt bother as I wanted to know if this is how I go about setting up the prob.

Also this one has stomped me as I dont know once again how to set this up.

The distribution of time taken to read through once and answer questions on a multiple choice exam is known to be normal with mean 65 min and standard deviation 15.2 min. How long should the test last if the examiners want to ensure that 95% of all those taking the exams have at least 10 min to check back over their work after going through the exam once?

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HallsofIvy
Homework Helper
Man I hate probability...anyhow could some help me with this Q as I am not understanding how to set it up...

Suppose that the force acting on a column which helps to support a building is normally distributed with mean 15.0 kips and standard deviation 1.25 kips:

What is the probability that the force differs from 15.0 kips by at most two standard deviations?

Do they mean this inequality:

12.5<F<17.5, where the < means greater than or equal to and > less than equal to
Yes, that is correct. Although it is easier to answer the question directly, taking standardized z to be between -2 and 2 read directly off theproblem.

It just came to me by the way

Oh i know i am suppose to standardize the raw variable I jus didnt bother as I wanted to know if this is how I go about setting up the prob.

Also this one has stomped me as I dont know once again how to set this up.

The distribution of time taken to read through once and answer questions on a multiple choice exam is known to be normal with mean 65 min and standard deviation 15.2 min. How long should the test last if the examiners want to ensure that 95% of all those taking the exams have at least 10 min to check back over their work after going through the exam once?
Find the time that 95% will take to do the problem, then add 10 min. What is the standard z so that P(z)= 0.95? Convert that to the "raw" t and add 10 minutes checking time.

Yea after I finished working the problem, I found that I should have simply just do it like that but I guess I wasnt thinking at the time.

As for the last one, would I reverse lookup the 0.95 as F(x) as thats what I interpreted it as and I got the x or z in your case to be approx. 1.6. I then found the raw data to be 89.32 mins and I added 10 to get 99.3 mins overall.

I have two more questions and then I am finished bothering you for awhile mon:

Find the following percentiles for the standard normal distribution. Interpolate where appropriate.

a)ninety-first
b)ninth

Jus help on whichever and I can do the rest

If the diameter of bearings produced by a certain machine has a normal distribution with sigma = 0.002 in, what is the probability that a randomly chosen bearing will have a diameter which differs from the mean diameter by at least 0.005 in.

How could I standardize dis seeing as how they havent given me the mean diameter or am I not seeing an easier way?

Dont know if this topic is being seen as read by others cause I havent gotten a response as yet but Halls sir could you look at my post before this again if thats not too much trouble.

HallsofIvy
Homework Helper
It's generally not a good idea to append a new problem to an old thread. People who feel the original question has been answered may not look at it again.

Find the following percentiles for the standard normal distribution. Interpolate where appropriate.

a)ninety-first
b)ninth
Yes, look up the z values so that P(z)= 0.91 and P(z)= 0.09.

If the diameter of bearings produced by a certain machine has a normal distribution with sigma = 0.002 in, what is the probability that a randomly chosen bearing will have a diameter which differs from the mean diameter by at least 0.005 in.
0.005 is 0.005/0.002= 2.5 standard deviations from the mean. Your standard z value will be 2.5. Since you are asked for the probability the diameter is at least 0.005 in from the mean, You are asked for P(z>= 2.5)= 1- P(z< 2.5).

Oh I see sir. I figured that was the problem since it wasnt look at as promptly as before. That suggestion will be duly noted nevertheless.

Thanks for all your work mon. You've been a big help.

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