Question

Find the value of z from the standard normal distribution that satisfies each of the following conditions. A. Area to the left of z=0.063 B. Area to the right of z=0.2981 C. Area between −z and z=0.5035

Answer 1

To find the values of z in the standard normal distribution that satisfy certain conditions based on area, we can use a standard normal table or z-table and apply the symmetry property of the distribution.

Step-by-step explanation:

A. To find the value of z that corresponds to an area to the left of z = 0.063 in the standard normal distribution, we need to look up this value using a standard normal table or a z-table. The value of z is approximately -1.48.

B. To find the value of z that corresponds to an area to the right of z = 0.2981, we can use the symmetry property of the standard normal distribution. The area to the right of z is equal to the area to the left of -z. So the value of z is approximately -0.2981.

C. To find the value of z that corresponds to an area between -z and z = 0.5035, we can use the symmetry property again. The area between -z and z is equal to twice the area to the left of z. So the value of z is approximately 0.6757.