How To Steal Register X Z

A z-table is a table that tells y'all what per centum of values fall below a certain z-score in a standard normal distribution.

A z-score merely tells you lot how many standard deviations away an individual information value falls from the mean. It is calculated every bit:

z-score = (x – μ) / σ

where:

x:private data value
μ:population mean
σ:population standard deviation

This tutorial shows several examples of how to utilise the z table.

Case ane

The scores on a sure college archway examination are normally distributed with hatefulμ = 82 and standard deviation σ = eight. Approximately what percentage of students score less than 84 on the exam?

Step 1: Find the z-score.

First, we will find the z-score associated with an exam score of 84:

z-score = (10 – μ) / σ = (84 – 82) / eight = 2 / 8 =0.25

Pace 2: Use the z-tabular array to observe the percentage that corresponds to the z-score.

Side by side, nosotros volition look up the value0.25in the z-table:

Example of how to read the z table

Approximately59.87%of students score less than 84 on this exam.

Example ii

The height of plants in a certain garden are normally distributed with a hateful of μ = 26.5 inches and a standard deviation of σ = 2.five inches. Approximately what per centum of plants are greater than 26 inches alpine?

Step 1: Notice the z-score.

Outset, nosotros volition detect the z-score associated with a top of 26 inches.

z-score = (10 – μ) / σ = (26 – 26.5) / 2.5 = -0.5 / 2.five = -0.2

Step 2: Employ the z-table to detect the percentage that corresponds to the z-score.

Next, we volition expect up the value -0.2 in the z-table:

Example of how to interpret z table

Nosotros encounter that 42.07% of values autumn below a z-score of -0.2. However, in this example nosotros desire to know what percentage of values are greaterthan -0.2, which we can discover past using the formula 100% – 42.07% = 57.93%.

Thus, aproximately59.87%of the plants in this garden are greater than 26 inches tall.

Case iii

The weight of a sure species of dolphin is normally distributed with a mean of μ = 400 pounds and a standard deviation of σ = 25 pounds. Approximately what percent of dolphins weigh betwixt 410 and 425 pounds?

Step 1: Find the z-scores.

Commencement, we will notice the z-scores associated with 410 pounds and 425 pounds

z-score of 410 = (10 – μ) / σ = (410 – 400) / 25 = x / 25 =0.4

z-score of 425 = (x – μ) / σ = (425 – 400) / 25 = 25 / 25 =i

Footstep 2: Use the z-table to find the percentages that corresponds to each z-score.

First, we volition wait up the value0.4 in the z-tabular array:

Example of using z table