# Can The Z Score Be Negative

### 95% of data values fall within two standard deviations of the mean. 99.7% of data values fall within three standard deviations of the mean.

(Source: www.statology.org)

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Typically, a score below 1.8 indicates that a company is likely heading for bankruptcy. Standard deviation is essentially a reflection of the amount of variability within a given data set.

Use this free online NegativeZscore chart to find the values of negative z-scores for the corresponding first and second digits after the decimal point of the score in the normal distribution table. The given negativezscore chart is used to look up standard normal probabilities.

Score: It is a way to compare individuals in a set of data. It shows how far away a particular score is from the group mean using standard deviation for that population to define the scale.

This has several uses, but the main one is that it allows us to start mapping observed scores onto probability values. For a given trial or set of trials, the classical probability of an event, assuming that all outcomes are equally likely, is the frequency of an event divided by the sample space, or total number of possible outcomes.

For example, in my book An Adventure in Statistics, the main character, Zach contemplates crossing the bridge of death. Therefore, the sample space for a single trial contains two events (alive or dead).

(Source: courses.lumenlearning.com)

Assuming these outcomes occur with equal frequency, then the classical probability of living is the frequency of living in the sample space (which is 1) divided by the total number of events in the sample space, 2. For example, when Zach contemplated crossing the bridge of death in my book, there were two possible outcomes: he lives or dies.

If I choose a sample of size 50 from the original population the probability that its mean will be more than 980 is nearly certain. Sep 4, 2014 Without looking at your question I will provide some basic information.

Negative values are on the left side tail, below the mean. However, with such large negative z-scores as -10.6 and -13.59, the probabilities can be darn close to 0 or 1. The difference between the two problems is whether you are finding the body or the tail.

Suppose you want to test the research question that cities in the south have experienced positive growth since 1980. Any sample of southern cities would come from a population distribution with a mean value greater than zero.

The alternative hypothesis to the null is that the population distribution contains a mean value less than or equal to zero. Suppose you want to compare growth in the northeast and the south.

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The difference between the mean growth rate of southern cities should be greater than the mean growth rate of northeast cities. Suppose you want to find the rejection region for the question regarding population growth in southern and northeast cities.

The t or z scores that are rejected are ones in the red region or positive values. If the null hypothesis states then the test statistics (score or t score) that rejects it is always population parameter is greater than zero (or a constant) negative and less than the score set for the rejection condition. Population parameter is less than zero (or a constant)positive and greater than the score set for the rejection condition.

Rejection region is in the negative section of the z (standard normal) distribution. To double-check mathematical's answer, compare the value of the test statistics to the information in the table.

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