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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.
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.
Answer:a) z = 1.96b) z = 1.96c) z = 0.61d) z = 1.12e) z = 0.44f) z = 0.44Step-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 tableWe get z = 1.96Therefore, a z score of 1.96 gives a probability of 0.9750b. The area between 0 and z is .4750Since 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 tableWe get z = 1.96Therefore, a z score of 1.96 gives a probability of 0.9750c. 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 tableWe get z = 0.61Therefore, a z score of 0.61 gives a probability of 0.7291d. The area to the right of z is .1314Since the area to the right of z is 0.1314, then the area to the left of z = 1 - 0.1314 = 0.8686This is gotten by determining the z score which gives a probability of 0.8686, This can be gotten from the z tableWe get z = 1.12Therefore, a z score of 1.12 gives a probability of 0.8686e. The area to the left of z is .6700This is gotten by determining the z score which gives a probability of 0.6700, This can be gotten from the z tableWe get z = 0.44Therefore, a z score of 0.44 gives a probability of 0.6700f. 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 = 0.6700This is gotten by determining the z score which gives a probability of 0.6700, This can be gotten from the z tableWe get z = 0.44Therefore, a z score of 0.44 gives a probability of 0.6700...