# How Do You Use a Z-Score Table for Probability Calculations?

• tsukuba
In summary, Mark44 found that the probability for X greater than 87 is 0.9192, and he keeps this value when solving for P(X > 87). Similarly, .1151 is the probability for X less than 74.
tsukuba

## Homework Statement

Let X be a normal random variable with mean 80 and standard deviation 5. What is the probability X is greater than 87? Less than 74?
I understand how to compute the z score but I'm confused as to when I have to keep the number from the z-table or subtract 1

z= x-μ /σ

## The Attempt at a Solution

z = 1.4
P (z > 87 ) = ??
I found the z score to be 0.9192 but do I keep this value as my answer or do I do 1 - 0.9192z=-1.2
P (z < 74)= ??
again, I found z score to be .1151
So I keep this value or 1 - 0.1151 and why?
Thank you

tsukuba said:

## Homework Statement

Let X be a normal random variable with mean 80 and standard deviation 5. What is the probability X is greater than 87? Less than 74?
I understand how to compute the z score but I'm confused as to when I have to keep the number from the z-table or subtract 1

## Homework Equations

z= x-μ /σ
You need parentheses when you write things like this. It should be z = (x - μ )/σ. As you wrote it, it would be interpreted as z = x - (μ /σ).
tsukuba said:

## The Attempt at a Solution

z = 1.4
P (z > 87 ) = ??
No, the above should be P(X > 87). You get the z-score by transforming the inequality, like so:
P(X > 87) = ##P(\frac{X - 80}{5} > \frac{87 - 80}{5}) = P(z > \frac{7}{5}) = P(z > 1.4)##

tsukuba said:
I found the z score to be 0.9192 but do I keep this value as my answer or do I do 1 - 0.9192
No, the z-score is 1.4, and the probability associated with it is 0.9192. This probability is the area under the standard normal curve (the "bell curve") between -∞ and 1.4.

It's very helpful to draw a quick sketch of the bell curve, including your z-score and the probability value you get from the table. With a sketch you can easily see which area under the curve you're interested in.
tsukuba said:
z=-1.2
P (z < 74)= ??
again, I found z score to be .1151
So I keep this value or 1 - 0.1151 and why?
Thank you

Last edited:
tsukuba said:

## Homework Statement

Let X be a normal random variable with mean 80 and standard deviation 5. What is the probability X is greater than 87? Less than 74?
I understand how to compute the z score but I'm confused as to when I have to keep the number from the z-table or subtract 1

z= x-μ /σ

## The Attempt at a Solution

z = 1.4
P (z > 87 ) = ??
I found the z score to be 0.9192 but do I keep this value as my answer or do I do 1 - 0.9192z=-1.2
P (z < 74)= ??
again, I found z score to be .1151
So I keep this value or 1 - 0.1151 and why?
Thank you

As Mark44 has said: draw a picture---even a very crude (but symmetric) picture will do. For any z, P(Z<z) is the area to the left of the point z under the graph of the unit normal density, so if z < 0, P(Z < z) < P(Z < 0) = 1/2, while P(Z > z) > P(Z > 0) = 1/2. So, if you are given a probability value P(Z < z ) < 1/2 or P(Z > z) > 1/2, you know that z < 0. If you are given the opposites of these, you know that z > 0.

Thank you both
Did well on my exam

## 1. What is a z-score table?

A z-score table is a statistical table that shows the probabilities associated with different z-scores. It is used to determine the probability of a particular value occurring in a normal distribution.

## 2. How do I use a z-score table?

To use a z-score table, you need to know the z-score of the value you are interested in and the area under the normal curve that you want to find the probability for. Locate the corresponding z-score in the table and read the probability from the corresponding row and column.

## 3. What is the purpose of a z-score table?

The purpose of a z-score table is to help calculate probabilities for a normal distribution. It is particularly useful in statistics and data analysis to determine the likelihood of a certain event occurring within a normal distribution.

## 4. Can I use a z-score table for non-normal distributions?

No, z-score tables are only applicable for normal distributions. For non-normal distributions, other methods, such as the central limit theorem or non-parametric statistics, may be used to calculate probabilities.

## 5. How accurate are z-score tables?

Z-score tables are considered very accurate for calculations involving normal distributions. However, they may not be as accurate for extreme or rare values, as the probability values in the table are often rounded to a certain number of decimal places.

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