If you have a variable whose distribution is approximately Gaussian (Normal), then the z-score gives the probability of observing a value that is equal to or more extreme. This is usually in the context of testing some hypothesis about the mean of the variable.
A very low probability would suggest that your hypothesis is wrong or that your assumptions about the data are wrong or that you have just had the misfortune of an unlikely event actually happening!
If the sample size is less then 30 use the T table, if greater then 30 use the Z table.
In a z-table, -0.625 corresponds to the area to the left of that z-score in the standard normal distribution. The value for -0.625 is approximately 0.2659. This means that about 26.59% of the data falls below a z-score of -0.625.
To find the probability associated with a z-score of 1.12, you can refer to the standard normal distribution table or use a calculator. A z-score of 1.12 corresponds to a cumulative probability of approximately 0.8686, meaning that about 86.86% of the data falls below this z-score. Therefore, the probability that a randomly selected value is less than a z-score of 1.12 is approximately 0.8686 or 86.86%.
z score = (test score - mean score)/SD z score = (87-81.1)/11.06z score = 5.9/11.06z score = .533You can use a z-score chart to calculate the probability from there.
If the Z-Score corresponds to the standard deviation, then the distribution is "normal", or Gaussian.
Not all z-score tables are the same. You must know how to use the specific table that you have.
A z table is used to calculate the probability of choosing something that is normally distributed. In order to use it, first a z score is needed. A z score is the number of standard distributions a value is away from the mean of the data. In order to find the z score, take the value of the datum, subtract the mean, then divide by the standard deviation. The result is a z score. Look up the z score on the table to find the probability of getting anything equal to or lesser than the value you chose.
If the sample size is less then 30 use the T table, if greater then 30 use the Z table.
You either look it up in a table of z scores or you can use a calculator such as the TI8 and use normalcdf.
In a z-table, -0.625 corresponds to the area to the left of that z-score in the standard normal distribution. The value for -0.625 is approximately 0.2659. This means that about 26.59% of the data falls below a z-score of -0.625.
The z-score is 0.84. In the related link, look in the body of the table for .3 area (.2995 closest) and it yields the .84 z-score.
To find the probability associated with a z-score of 1.12, you can refer to the standard normal distribution table or use a calculator. A z-score of 1.12 corresponds to a cumulative probability of approximately 0.8686, meaning that about 86.86% of the data falls below this z-score. Therefore, the probability that a randomly selected value is less than a z-score of 1.12 is approximately 0.8686 or 86.86%.
Assume the z-score is relative to zero score. In simple terms, assume that we have 0 < z < z0, where z0 is the arbitrary value. Then, a negative z-score can be greater than a positive z-score (yes). How? Determine the probability of P(-2 < z < 0) and P(0 < z < 1). Then, by checking the z-value table, you should get: P(-2 < z < 0) ≈ 0.47725 P(0 < z < 1) ≈ 0.341345
z score = (test score - mean score)/SD z score = (87-81.1)/11.06z score = 5.9/11.06z score = .533You can use a z-score chart to calculate the probability from there.
If the Z-Score corresponds to the standard deviation, then the distribution is "normal", or Gaussian.
1.75 using table for standard normal cumulative probabilities
The z-score that corresponds to P78 (the 78th percentile) can be found using a standard normal distribution table or calculator. It indicates that 78% of the data falls below this z-score. For a standard normal distribution, the z-score for P78 is approximately 0.77. This means that a value at the 78th percentile is about 0.77 standard deviations above the mean.