Standard Deviation: Get 10 Cents on Probability Problem

In summary, the conversation was about a problem in statistics and finding the probability using z-scores and a standard normal curve. The final answer was 2.14%, but when entered into an online schooling system, it was not accepted. The conversation ended with a possible explanation for the discrepancy and the issue being resolved.
  • #1
Coder74
20
0
Hey everyone!

I'm learning about some statistics and its past office hours with my teacher but I'm stuck on this problem.. I came up with 2.14% as the probabillity\final answer..
Could you guys give me your 10 cents on this?

Thanks again!

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  • #2
You need to convert the two raw data (called $x$) into $z$-scores:

\(\displaystyle z=\frac{x-\mu}{\sigma}\)

Then, use a table to find the area under th standard normal curve between the two $x$-scores to find the requested probability.

Can you proceed?
 
  • #3
Coder74 said:
Hey everyone!

I'm learning about some statistics and its past office hours with my teacher but I'm stuck on this problem.. I came up with 2.14% as the probabillity\final answer..
Could you guys give me your 10 cents on this?

Thanks again!

Hi Coder74,

2.14% is the correct answer.
It's the probability between 2 and 3 standard deviations from the mean.
 
  • #4
Thanks for both replies you guys I appreciate it!
However since this is an online schooling when I entered 2.14 as an answer it wouldn't register as correct..
 
  • #5
Coder74 said:
Thanks for both replies you guys I appreciate it!
However since this is an online schooling when I entered 2.14 as an answer it wouldn't register as correct..

Consulting the table in my old stats textbook, I find:

\(\displaystyle P(X)\approx0.4987-0.4772=0.0215\)

When I use a numeric scheme to approximate the integral I get:

\(\displaystyle P(X)=\frac{1}{\sqrt{2\pi}}\int_2^3 e^{-\frac{x^2}{2}}\,dx\approx0.0214002339165491\)

Perhaps this issue is you are entering a percentage, and the app is expecting the value of probability, i.e. 0.0214. :D
 
  • #6
Thanks, Mark! As it turns out there was a glitch in the system after all.. Haha, thanks for the help everyone!
 

FAQ: Standard Deviation: Get 10 Cents on Probability Problem

What is standard deviation?

Standard deviation is a measure of how spread out a set of data is from its mean. It tells us how much the data points deviate from the average, or how much they vary from each other.

How is standard deviation calculated?

Standard deviation is calculated by taking the square root of the variance. The variance is the average of the squared differences between each data point and the mean.

Why is standard deviation important?

Standard deviation is important because it helps us understand the variability of data. It allows us to compare and analyze data sets, and make predictions based on the likelihood of certain values occurring.

What does a high standard deviation indicate?

A high standard deviation indicates that the data points are spread out over a larger range from the mean, and there is more variability in the data. This means that the data points are more diverse and less likely to be close to the average.

How can standard deviation be used in probability problems?

Standard deviation can be used in probability problems to calculate the likelihood of a certain event occurring. It tells us how much the data points deviate from the mean, which can help us determine the probability of a specific outcome or range of outcomes.

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