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Find the percent of the total area under the standard normal curve between the following​ z-scores.

z= -1.5 and z= -0.65

User TeaNyan
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1 Answer

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Final answer:

The percent of the total area under the standard normal curve between z-scores of -1.5 and -0.65 is found by subtracting the area to the left of z=-1.5 from the area to the left of z=-0.65, which equals 0.1910 or 19.10% when expressed as a percentage.

Step-by-step explanation:

To find the percent of the total area under the standard normal curve between z=-1.5 and z=-0.65, we refer to a z-table which shows the area under the curve to the left of a given z-score. For z=-1.5, find the corresponding area on the z-table. For z=-0.65, again find the respective area.

The area to the left of z=-1.5 is typically found to be approximately 0.0668, and the area to the left of z=-0.65 is about 0.2578. To determine the area between these two z-scores, subtract the smaller area from the larger area:

Area between z=-1.5 and z=-0.65 = Area to the left of z=-0.65 - Area to the left of z=-1.5
= 0.2578 - 0.0668
= 0.1910

To express this as a percent, multiply by 100:

(0.1910 × 100)
= 19.10%

Therefore, the percent of the total area under the standard normal curve between z=-1.5 and z=-0.65 is 19.10%.

User Narendra Parmar
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