Continuous Random Variables and Prob. Distribution

In summary, the conversation discusses the use of probability in various scenarios. The first problem involves finding the probability that a force acting on a building differs from its mean by at most two standard deviations. The second problem deals with determining the length of a multiple choice exam in order to ensure that 95% of test takers have at least 10 minutes to check their work. The conversation also includes a question about finding percentiles for the standard normal distribution and a problem involving the probability of a bearing's diameter differing from the mean by a certain amount.
  • #1
Suitengu
46
0
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 don't 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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  • #2
Suitengu said:
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 don't 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.
 
  • #3
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 that's 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 haven't given me the mean diameter or am I not seeing an easier way?
 
  • #4
Dont know if this topic is being seen as read by others cause I haven't gotten a response as yet but Halls sir could you look at my post before this again if that's not too much trouble.
 
  • #5
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).
 
  • #6
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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1. What is a continuous random variable?

A continuous random variable is a type of variable in statistics that can take on any value within a certain range, as opposed to discrete random variables which can only take on specific values. Examples of continuous random variables include height, weight, and temperature.

2. What is a probability distribution?

A probability distribution is a function that assigns a probability to each possible outcome of a random variable. It shows the likelihood of each outcome occurring and is typically represented graphically as a curve or histogram.

3. How is a continuous random variable different from a discrete random variable?

A continuous random variable can take on any value within a range, while a discrete random variable can only take on specific values. Continuous random variables are typically measured, while discrete random variables are typically counted.

4. What is the difference between a probability density function and a cumulative distribution function?

A probability density function (PDF) is a function that describes the relative likelihood of a continuous random variable taking on a certain value. A cumulative distribution function (CDF) is a function that gives the probability that a continuous random variable will be less than or equal to a certain value.

5. How do you calculate the expected value of a continuous random variable?

To calculate the expected value of a continuous random variable, you multiply each possible value by its probability and then sum all of the products. This is similar to how you would calculate the mean of a set of numbers, but with probabilities instead of values.

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