for a standard normal curve, find the z-score that separates the bottom 30% from the top 70%
In the back of your statistics text, there is a table labeled something like "areas under the normal distribution." Remembering that the Z score will be negative because it is below the mean, use it to find the Z value that has either .30 for the smaller side or .70 for the larger side.
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To find the z-score that separates the bottom 30% from the top 70% of a standard normal curve, you can use the z-table or a statistical calculator.
1. Start by subtracting 30% (0.30) from 1 (to find the area to the right of the z-score).
1 - 0.30 = 0.70
2. Divide the result by 2 to get the area for each tail of the z-score.
0.70 / 2 = 0.35
3. Look up the closest value to the resulting area (0.35) in the z-table. The z-score will correspond to this area.
From the z-table, the closest value to 0.35 is approximately 0.37.
Therefore, the z-score that separates the bottom 30% from the top 70% of a standard normal curve is approximately 0.37.
To find the z-score that separates the bottom 30% from the top 70% of a standard normal curve, you can use a standard normal distribution table or a statistical calculator.
Here's how you can use a standard normal distribution table to find the z-score:
1. Identify the area under the curve. In this case, the bottom 30% means you want to find the z-score that corresponds to the area to the left of that value.
2. Look up the value for the probability in the table. Since the table gives values for the area to the left of a given z-score, we need to find the z-score that corresponds to an area of 0.30.
3. Locate the closest value in the table to 0.30. In this case, the closest value is 0.3005, which corresponds to a z-score of approximately -0.52.
4. Since the problem wants to separate the bottom 30% from the top 70%, you need to find the z-score that corresponds to the area to the right of -0.52. Subtract the z-score you found in step 3 from 0 to get the z-score that separates the top 70% from the bottom 30%. So, the z-score that separates the bottom 30% from the top 70% is approximately +0.52.
Remember, you can also use a statistical calculator or software to find this z-score directly by entering the probabilities or area values.