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Answer:
The area under the standard normal curve to the right of z = 1 is 0.1587.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X, which is also the area to the left of z. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X, which is also the area to the right of x.
Area to the right of z = 1.
1 subtracted by the pvalue of z = 1.
z = 1 has a pvalue of 0.8413
1 - 0.8413 = 0.1587
The area under the standard normal curve to the right of z = 1 is 0.1587.
The area under the standard normal curve to the right of the z-score of 1 is 0.1587.
How to find area under standard normal curve for z-score?
To find the area under the standard normal curve for given z-score, first find out the area under to the left of the z, and then subtract it with 1.
The area under the standard normal curve to the right of z = 1. Follow steps below to find the area under the standard normal curve to the right of z = 1.
- Step 1- Find the area to the left of the z,
Choose the positive z values, as the given z-score of 1 is also positive. In the attached image, the value of z at 1 is 0.8413. Hence, the area at the left is,
[tex]A_l=0.8413[/tex]
- Step 2- Find the area to the right
The total area under the bell curve is 1. Hence, subtract the above area of left from number 1 to find the area to the right.
[tex]A_r=1-0.8413\\A_r=0.1587[/tex]
Hence, the area under the standard normal curve to the right of the z-score of 1 is 0.1587.
Learn more about the z-score here;
https://brainly.com/question/13299273
