# Statistics MCQs – Continuous Distributions Part 10

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181. If P (Z > z) = 0.6844 what is the value of z (z has a standard normal distribution) ?

a. -0.48

b. 0.48

c. -1.04

d. 1.04

e. -0.21

Answer: A

182. If P (Z < z) = 0.6844 what is the value of z (z has a standard normal distribution) ?

a. -0.48

b. 0.48

c. -1.04

d. 1.04

e. -0.21

Answer: B

183. If P (Z > z) = 0.8508 what is the value of z (z has a standard normal distribution) ?

a. -0.48

b. 0.48

c. -1.04

d. 1.04

e. -0.21

Answer: C

184. If P (Z < z) = 0.8508 what is the value of z (z has a standard normal distribution) ?

a. -0.48

b. 0.48

c. -1.04

d. 1.04

e. -0.21

Answer: D

185. If P (Z > z) = 0.5832 what is the value of z (z has a standard normal distribution) ?

a. -0.48

b. 0.48

c. -1.04

d. 1.04

e. -0.21

Answer: E

186. If P (Z < z) = 0.5832 what is the value of z (z has a standard normal distribution) ?

a. -0.48

b. 0.48

c. -1.04

d. 1.04

e. 0.21

Answer: E

187. If P (Z > z) = 0.9830 what is the value of z (z has a standard normal distribution) ?

a. -2.12

b. 2.12

c. -1.77

d. 1.77

e. -0.21

Answer: A

188. If P (Z < z) = 0.9830 what is the value of z (z has a standard normal distribution) ?

a. -2.12

b. 2.12

c. -1.77

d. 1.77

e. -0.21

Answer: B

189. If P (Z > z) = 0.9616 what is the value of z (z has a standard normal distribution) ?

a. -2.12

b. 2.12

c. -1.77

d. 1.77

e. -0.21

Answer: C

190. If P (Z < z) = 0.9616 what is the value of z (z has a standard normal distribution) ?

a. -2.12

b. 2.12

c. -1.77

d. 1.77

e. -0.21

Answer: D

191. Given that z is a standard normal random variable and that the area to the left of z is 0.305, then the value of z is:

a. 0.51

b. -0.51

c. 0.86

d. -0.86

Answer: B

e. 0.24

192. The diameters of oranges found in the orchard of an orange farm follow a normal distribution with a mean of 120mm and a standard deviation of 10mm. The smallest 10 % of oranges (those with the smallest diameters) cannot be sold and are therefore given away. What is the cut-off diameter in this case if oranges with the smallest 10 % of diameters are to be given away?

a. 107.2

b. 103.6

c. 111.6

d. 109.6

e. 105.9

Answer: A

193. The diameters of oranges found in the orchard of an orange farm follow a normal distribution with a mean of 120mm and a standard deviation of 10mm. The smallest 5 % of oranges (those with the smallest diameters) cannot be sold and are therefore given away. What is the cut-off diameter in this case if oranges with the smallest 5 % of diameters are to be given away?

a. 107.2

b. 103.6

c. 111.6

d. 109.6

e. 105.9

Answer: B

194. The diameters of oranges found in the orchard of an orange farm follow a normal distribution with a mean of 120mm and a standard deviation of 10mm. The smallest 20 % of oranges (those with the smallest diameters) cannot be sold and are therefore given away. What is the cut-off diameter in this case if oranges with the smallest 20 % of diameters are to be given away?

a. 107.2

b. 103.6

c. 111.6

d. 109.6

e. 105.9

Answer: C

195. The diameters of oranges found in the orchard of an orange farm follow a normal distribution with a mean of 120mm and a standard deviation of 10mm. The smallest 15 % of oranges (those with the smallest diameters) cannot be sold and are therefore given away. What is the cut-off diameter in this case if oranges with the smallest 15 % of diameters are to be given away?

a. 107.2

b. 103.6

c. 111.6

d. 109.6

e. 105.9

Answer: D

196. The diameters of oranges found in the orchard of an orange farm follow a normal distribution with a mean of 120mm and a standard deviation of 10mm. The smallest 8 % of oranges (those with the smallest diameters) cannot be sold and are therefore given away. What is the cut-off diameter in this case if oranges with the smallest 8 % of diameters are to be given away?

a. 107.2

b. 103.6

c. 111.6

d. 109.6

e. 105.9

Answer: E

197. The diameters of oranges found in the orchard of an orange farm follow a normal distribution with a mean of 120mm and a standard deviation of 10mm. The farmer would like to select the largest 10 % of oranges (those with the largest diameters) in order to be able to keep them for himself and his family to enjoy! What is the cut-off diameter in this case if oranges with the largest 10 % of diameters are to be kept?

a. 132.8

b. 136.4

c. 128.4

d. 130.4

e. 134.1

Answer: A

198. The diameters of oranges found in the orchard of an orange farm follow a normal distribution with a mean of 120mm and a standard deviation of 10mm. The farmer would like to select the largest 5 % of oranges (those with the largest diameters) in order to be able to keep them for himself and his family to enjoy! What is the cut-off diameter in this case if oranges with the largest 5 % of diameters are to be kept?

a. 132.8

b. 136.4

c. 128.4

d. 130.4

e. 134.1

Answer: B

199. The diameters of oranges found in the orchard of an orange farm follow a normal distribution with a mean of 120mm and a standard deviation of 10mm. The farmer would like to select the largest 20 % of oranges (those with the largest diameters) in order to be able to keep them for himself and his family to enjoy! What is the cut-off diameter in this case if oranges with the largest 20 % of diameters are to be kept?

a. 132.8

b. 136.4

c. 128.4

d. 130.4

e. 134.1

Answer: C

200. The diameters of oranges found in the orchard of an orange farm follow a normal distribution with a mean of 120mm and a standard deviation of 10mm. The farmer would like to select the largest 15 % of oranges (those with the largest diameters) in order to be able to keep them for himself and his family to enjoy! What is the cut-off diameter in this case if oranges with the largest 15 % of diameters are to be kept?

a. 132.8

b. 136.4

c. 128.4

d. 130.4

e. 134.1

Answer: D