Basic Z-Score & Standard Normal Question

In summary, the conversation involves finding probabilities for a standard normal distribution using a calculator and a book. The speaker is unsure about the answers given in the book and questions whether there may be a mistake. They provide their own calculations and express confusion about the given answers.
  • #1
kuahji
394
2
If Z is a random variable having the standard normal distribution, find
P(Z[tex]\geq[/tex]-.79)

So I punch it into my calculator nmcdf(-.79,infinity,0,1) & I get the answer .7852

The book however has the answer .2148 (essentially 1-ans).

Which is what I don't understand...

Have I forgotten something really simple, or do you think there is an error in the book. Most of the time its me :(.
 
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  • #2
Also, P(-1.90>z>.44)

The only thing I could think of was nmcdf(-infinity,-1.90,0,1)+nmcdf(.44,infinity,0,1) which gives .3587 but the book gives the answer .6143.
 
  • #3
Are you sure you've written the problems correctly? P(-1.90>z>.44) is obviously zero, no matter how z is distributed.
 
Last edited:
  • #4
Hurkyl said:
Are you sure you've written the problems correctly? P(-1.90>z>.44) is obviously zero, no matter how z is distributed.

100% sure. I think its an error in the book... I don't really see how it can be possible. If you flip the signs around it makes sense though.
 

1. What is a basic z-score?

A z-score, or standard score, is a statistical measure that indicates how many standard deviations a data point is above or below the mean of a dataset. It is a way to standardize and compare data with different units and scales.

2. How do you calculate a z-score?

To calculate a z-score, you need to know the data point's value, the mean of the dataset, and the standard deviation. The formula for z-score is: (data point - mean) / standard deviation. This will give you the number of standard deviations the data point is away from the mean.

3. What is the standard normal distribution?

The standard normal distribution is a specific type of probability distribution where the mean is 0 and the standard deviation is 1. It is also known as the z-distribution and is often used in statistics to analyze and compare data.

4. How is the standard normal distribution related to z-scores?

Z-scores are calculated based on the standard normal distribution. A z-score of 0 indicates that the data point is at the mean of the distribution, while a z-score of 1 means the data point is 1 standard deviation above the mean. This allows us to interpret z-scores in relation to the standard normal distribution.

5. Why is the standard normal distribution important?

The standard normal distribution is important because it allows us to compare and analyze data from different datasets with different units and scales. It also helps us to make predictions and calculate probabilities in statistics. Additionally, many statistical tests and models are based on the assumption of a normal distribution, making the standard normal distribution a fundamental concept in statistics.

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