Given that z is a standard normal random variable, find z for each situation. a. The area to the left of z is .9750. b. The area between 0 and z is .4750. c. The area to the left of z is .7291. d. The area to the right of z is .1314. e. The area to the left of z is .6700. f. The area to the right of z is .3300.

a) z = 1.96

b) z = 1.96

c) z = 0.61

d) z = 1.12

e) z = 0.44

f) z = 0.44

Step-by-step explanation:

a. The area to the left of z is .9750.

This is gotten by determining the z score  which gives a probability of 0.9750, This can be gotten from the z table

We get z = 1.96

Therefore, a z score of 1.96 gives a probability of 0.9750

b. The area between 0 and z is .4750

Since the area between 0 and z is .4750, then the area to the left of z = 0.4750 + 0.500 = 0.9750.

This is gotten by determining the z score  which gives a probability of 0.9750, This can be gotten from the z table

We get z = 1.96

Therefore, a z score of 1.96 gives a probability of 0.9750

c. The area to the left of z is .7291.

This is gotten by determining the z score  which gives a probability of 0.7291, This can be gotten from the z table

We get z = 0.61

Therefore, a z score of 0.61 gives a probability of 0.7291

d. The area to the right of z is .1314

Since the area to the right of z is 0.1314, then the area to the left of z = 1 - 0.1314 = 0.8686

This is gotten by determining the z score  which gives a probability of 0.8686, This can be gotten from the z table

We get z = 1.12

Therefore, a z score of 1.12 gives a probability of 0.8686

e. The area to the left of z is .6700

This is gotten by determining the z score  which gives a probability of 0.6700, This can be gotten from the z table

We get z = 0.44

Therefore, a z score of 0.44 gives a probability of 0.6700

f. The area to the right of z is .3300.

Since the area to the right of z is 0.1314, then the area to the left of z = 1 - 0.3300 = 0.6700

This is gotten by determining the z score  which gives a probability of 0.6700, This can be gotten from the z table

We get z = 0.44

Therefore, a z score of 0.44 gives a probability of 0.6700

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