Find the indicated z score shown in the graph calculator

Question

Video Transcript

Key, they are welcome to numerade, so we are given a problem here where we have the area under the curve and normal distribute bute curve, and we are given a probability of 0.0749, so we're acted, find a score and round to 2 decimal places. So with this, we have the probability of x since his right tail we're going to do greater than z, which is equal to the probability of 0.0749. All right, so we're looking for the z score here so with the right tail z score. We'Re going to look at our table or use your calculator and we should get a score that is around 1.4 4 point. Okay, so this makes sense because our z square here is positive and it is this much standard deviations away from the mean right. So we can write positive and greater than mean, so we could do greater than man okay, so this makes sense. So our answer here would be z. Equals 1.44 itsomethi helps and have a great day.

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Video Transcript
Example 1: Find Z-Score Given Area to the Left
Example 2: Find Z-Score Given Area to the Right
Example 3: Find Z-Scores Given Area Between Two Values
How do you find the indicated z

There are three ways to find the z-score that corresponds to a given area under a normal distribution curve

1. Use the z-table.

2. Use the Percentile to Z-Score Calculator.

3. Use the invNorm() Function on a TI-84 Calculator.

The following examples show how to use each of these methods to find the z-score that corresponds to a given area under a normal distribution curve.

Example 1: Find Z-Score Given Area to the Left

Find the z-score that has 15.62% of the distribution’s area to the left.

Method 1: Use the z-table.

The z-score that corresponds to a value of .1562 in the z-table is -1.01.

2. Use the Percentile to Z-Score Calculator.

According to the Percentile to Z-Score Calculator, the z-score that corresponds to a percentile of .1562 is -1.01.

3. Use the invNorm() function on a TI-84 calculator.

Using the invNorm() function on a TI-84 calculator, the z-score that corresponds to an area of .1562 to the left is -1.01.

Notice that all three methods lead to the same result.

Example 2: Find Z-Score Given Area to the Right

Find the z-score that has 37.83% of the distribution’s area to the right.

Method 1: Use the z-table.

The z table shows the area to the left of various z-scores. Thus, if we know the area to the right is .3783 then the area to the left is 1 – .3783 = .6217

The z-score that corresponds to a value of .6217 in the z-table is .31

2. Use the Percentile to Z-Score Calculator.

According to the Percentile to Z-Score Calculator, the z-score that corresponds to a percentile of .6217 is .3099.

3. Use the invNorm() function on a TI-84 calculator.

Using the invNorm() function on a TI-84 calculator, the z-score that corresponds to an area of .6217 to the left is .3099.

Example 3: Find Z-Scores Given Area Between Two Values

Find the z-scores that have 95% of the distribution’s area between them.

Method 1: Use the z-table.

If 95% of the distribution is located between two z-scores, it means that 5% of the distribution lies outside of the z-scores.

Thus, 2.5% of the distribution is less than one of the z-scores and 2.5% of the distribution is greater than the other z-score.

Thus, we can look up .025 in the z-table. The z-score that corresponds to .025 in the z-table is -1.96.

Thus, the z-scores that contain 95% of the distribution between them are -1.96 and 1.96.

2. Use the Percentile to Z-Score Calculator.

According to the Percentile to Z-Score Calculator, the z-score that corresponds to a percentile of .025 is -1.96.

Thus, the z-scores that contain 95% of the distribution between them are -1.96 and 1.96.

3. Use the invNorm() function on a TI-84 calculator.

Using the invNorm() function on a TI-84 calculator, the z-score that corresponds to an area of .025 to the left is -1.96.

Thus, the z-scores that contain 95% of the distribution between them are -1.96 and 1.96.

How do you find the indicated z

How do you calculate the z-score? The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation. As the formula shows, the z-score is simply the raw score minus the population mean, divided by the population standard deviation.