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Answer :
Final answer:
0.4554.
Explanation:
To find the area between z = 0 and z = 1.70 for a standard normal distribution, one must use the Z-table. The standard normal distribution has a mean (μ) of 0 and a standard deviation (σ) of 1. By checking a Z-table, one can find the area under the curve to the left of the z-score of 1.70. This value, when subtracted from the area to the left of z = 0 (which is always 0.5 since it's the median of the distribution), gives us the area between these two z-scores.
Assuming the area to the left of z = 1.70 is approximately 0.9554 (which might vary slightly based on different Z-tables), the calculation would be: 0.9554 (area to the left of z = 1.70) - 0.5 (area to the left of z = 0). Therefore, the area between z = 0 and z = 1.70 would be approximately 0.4554.
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Final answer:
The area between z = 0 and z = 1.70 within a standard normal distribution is approximately 0.4554, which is obtained by checking the cumulative area at z = 1.70 (0.9554) and subtracting the cumulative area at z = 0 (0.5).
Explanation:
In order to find the area between z = 0 and z = 1.70 for a standard normal distribution, we can use a Z-table or appropriate statistical software. For a standard normal distribution, a z-score of 0 corresponds to the mean and thus lies exactly in the middle of the distribution. Since a standard normal distribution is symmetric, the area to the left of z = 0 is 0.5 or 50% of the total area under the curve.
If we want to find the area between z = 0 and z = 1.70, we would subtract the cumulative area at z = 0 from the cumulative area at z = 1.70. Referring to the Z-table or using statistical software should give a cumulative area of approximately 0.9554 for z = 1.70. Thus, the area between z = 0 and z = 1.70 would be 0.9554 - 0.5 = 0.4554.
Therefore, the area between z = 0 and z=1.70 in the standard normal distribution is approximately 0.4554, rounded to four decimal places.
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