Question

Find the z-score such that: a. The area under the standard normal curve to its left is 0.5 b. The area under the standard normal curve to its left is 0.9826 c. The area under the standard normal curve to its right is 0.1423 z

Answer 1

Answer:

The answer is below

Step-by-step explanation:

The z score is used to determine by how many standard deviations the mean is above or below the raw score. If the z score is positive then the raw score is above the mean while if the z score is negative then the raw score is below the mean. The z score is given by:

$z=\frac{x-\mu}{\sigma}\\ \\\mu=mean, \sigma=standard\ deviation$

a)

From the normal distribution, 0.5 corresponds to a z score of 0.

z = 0.

b) From the normal distribution, an area of 0.9826 to the left corresponds to a z score of 2.11.

c) An area to the right of 0.1423 = an area of 0.8577 ( 1- 0.1423) to the left.  From the normal distribution, an area of 0.8577 to the left corresponds to a z score of 1.07