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Answer :
Final answer:
To find the area under the standard normal curve between z=0.35 and z=1.37, we find the areas to the left of each z-score using the Z-table and subtract them to get the area between these z-scores, which is 0.2779.
Explanation:
In order to find the area under the standard normal curve to the left of z=0.35 and to the right of z=1.37, we need to use the Z-table (also known as the standard normal table). The Z-table holds cumulative probabilities for a standard normal distribution. In other words, each entry in the table represents the area under the curve for values less than or equal to the z-score.
Referring to the Z-table, the area to the left of z=0.35 is approximately 0.6368 and the area to the left of z=1.37 is approximately 0.9147. Since we’re looking for the area to the right of z=1.37, we subtract this value from 1 as the total area under the curve is 1. Therefore, 1 - 0.9147 = 0.0853 is the area to the right of z=1.37.
So, the area under the curve between z=0.35 and z=1.37 is the difference between the two areas 0.9147 (area to the left of z=1.37) and 0.6368 (area to the left of z=0.35), which is 0.9147 - 0.6368 = 0.2779.
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The area under the standard normal curve to the left of z=0.35 and to the right of z=1.37 is approximately 0.7221. This is obtained by finding the area values from the z-table or using statistical software and adding them.
This question requires you to use the properties of the standard normal curve to calculate the area. In the Standard Normal curve, the total area under the curve is equal to 1. The area to the left of z=0 is 0.5. To obtain the areas to the left of z=0.35 and right of z=1.37, we look them up in the z-table or use statistical software.
From the z-table, we find that the area to the left of z=0.35 is approximately 0.6368. The area to the left of z=1.37 is approximately 0.9147. Since the total area under the curve is 1, the area to the right of z=1.37 is 1-0.9147 =0.0853.
Finally, the area under the standard normal curve either to the left of z=0.35 or to the right of z=1.37 is calculated by adding both areas - 0.6368 + 0.0853 = 0.7221. Therefore, the answer to your question is about 0.7221, rounding to the nearest four decimal places where necessary.
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