Probability over an interval in a Normal Distribution?

In summary: The CDF is usually given in tabular form, since there is no analytic solution. The table (standard normal) will be for mean = 0 and standard deviation = 1. Your data then is for the range -.28/.12 to .22/.12. The probability that it will take anywhere from 16.00 to 16.50 seconds to develop one of the prints is approximately 0.2594. In summary, the given conversation discusses the probability of developing a print within a certain time interval in a photographic process with a normal distribution. The CDF (Cumulative Distribution Function) and its integral are used to find the probability, which is approximately 0.2594.
  • #1
adamwitt
25
0
I've been given the question:
In a photographic process, the developing time of prints may be looked upon as
a random variable which is normally distributed with a mean of 16.28 seconds
and a standard deviation of 0.12 second. Find the probability that it will take
anywhere from 16.00 to 16.50 seconds to develop one of the prints.

I *think* I know what I need to do, just don't know how to do it:

So I have the Guassian Distribution formula (with std dev & mean plugged in) as my Probability Density Function.
I need to find the area under the Cumulative Distribution Function over the interval 16 to 16.50.
Because the integrals in CDFs are evaluated from -inf to a, I need to subtract the (integral of CDF from -inf to 16) from the (integral of CDF from -inf to 16.50), and that will be my answer.

But I don't know how to (A) Get the CDF, (B) Evaluate the CDF integral.

Ive tried reading up on the net but I'm not following the theory, can someone please show me how to do this? Thank you!EDIT+=======
Apologies, realized i posted it on the wrong board! feel free to ignore / delete. Please see my post over in the correct homework calculus thread! thank you!
 
Last edited:
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  • #2
The CDF is usually given in tabular form, since there is no analytic solution. The table (standard normal) will be for mean = 0 and standard deviation = 1. Your data then is for the range -.28/.12 to .22/.12.
 

What is the Normal Distribution?

The Normal Distribution is a probability distribution that is often used in statistics to represent a large set of data. It is characterized by a bell-shaped curve and is symmetric around the mean. Many natural phenomena, such as height and IQ, follow a Normal Distribution.

What is the Probability over an interval in a Normal Distribution?

The Probability over an interval in a Normal Distribution represents the likelihood that a data point falls within a certain range of values. This can be calculated by finding the area under the curve for that interval.

How do you calculate Probability over an interval in a Normal Distribution?

To calculate Probability over an interval in a Normal Distribution, you first need to know the mean and standard deviation of the data set. Then, you can use a formula or a statistical software to find the area under the curve for the desired interval. This will give you the probability of a data point falling within that interval.

What is the z-score in a Normal Distribution?

The z-score, also known as the standard score, is a measure of how many standard deviations a data point is away from the mean in a Normal Distribution. It is calculated by subtracting the mean from the data point and dividing by the standard deviation. A positive z-score indicates that the data point is above the mean, while a negative z-score indicates it is below the mean.

How does the Central Limit Theorem relate to Normal Distribution?

The Central Limit Theorem states that when independent random variables are added, their sum tends to follow a Normal Distribution. This is why the Normal Distribution is often used to analyze data, as it can approximate the distribution of many different types of data.

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