Question

Given that z is a standard normal random variable, find z for each situation. (Round your answers to two decimal places.) (a) The area to the left of z is 0.2743. (b) The area between -z and z is 0.9534 (c) The area between -z and z is 0.2052 (d) The area to the left of z is 0.9952.

Answer 1

To find the value of z for each situation, we can use the Z-table to locate the corresponding area under the normal curve.

Step-by-step explanation:

To find the value of z for each situation, we can use the Z-table to locate the corresponding area under the normal curve.

(a) The area to the left of z is 0.2743. Using the Z-table, we can find the z-score that corresponds to this area, which is approximately -0.61.

(b) The area between -z and z is 0.9534. This means that the area to the left of z is (1 - 0.9534)/2 = 0.0233. Using the Z-table, we can find the z-score that corresponds to this area, which is approximately -1.98. Therefore, z is -1.98.

(c) The area between -z and z is 0.2052. This means that the area to the left of z is (1 - 0.2052)/2 = 0.3974. Using the Z-table, we can find the z-score that corresponds to this area, which is approximately -0.26. Therefore, z is -0.26.

(d) The area to the left of z is 0.9952. Using the Z-table, we can find the z-score that corresponds to this area, which is approximately 2.57.

Answer 2

To find the corresponding z-score for each situation, use the z-table.

Step-by-step explanation:

A Z score, also known as standard score, measures how many standard deviations a data point is from the mean of a dataset. It helps assess a data point's relative position. To find the corresponding z-score for each situation, we can use the z-table. The z-table shows the area under the normal curve to the left of a given z-score.

(a) The z-score for an area to the left of 0.2743 is approximately -0.61.

(b) The z-score for an area between -z and z of 0.9534 is approximately 1.96.

(c) The z-score for an area between -z and z of 0.2052 is approximately 0.79.

(d) The z-score for an area to the left of 0.9952 is approximately 2.58.