Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

Let Z be the standard normal random variable. Find z>0 so that the area between

ID: 3056231 • Letter: L

Question

Let Z be the standard normal random variable. Find z>0 so that the area between -z and +z is 0.99.

1.28

1.645

1.96

2.33

2.575

Let Z be the standard normal random variable. Find z so that the area to the left of z is 0.3156.

-0.80

-1.18

-0.48

1.28

None of the above

Let Z be the standard normal random variable. What is P(Z>-2.38)?

0.5239

0.7764

0.9162

0.9913

None of the above

Let Z be the standard normal random variable. What is P(Z>0.38)?

0.0087

0.0708

0.0838

0.1075

None of the above

Let Z be the standard normal random variable. What is P(1<Z<1.50)?

0.0640

0.1938

0.1579

0.0919

None of the above

Let Z be the standard normal random variable. What is P(Z<-0.38)?

0.0571

0.0918

0.1401

0.3520

None of the above

Let Z be the standard normal random variable. What is P(Z<1.38)?

0.5239

0.7764

0.9162

0.9913

None of the above

  

Explanation / Answer

a) P(-z < Z < z) = 0.99

or, P(Z < z) - P(Z < -z) = 0.99

or, P(Z < z) - (1 - P(Z < z)) = 0.99

or, 2*P(Z < z) - 1 = 0.99

or, P(Z < z) = 0.995

or, z = 2.575

Option-E) 2.575

b) P(Z < z) = 0.3156

or, z = -0.48

Option-C) -0.48

c) P(Z > -2.38) = 1 - P(Z < -2.38) = 1 - 0.0087 = 0.9913

Option-D) 0.9913

d) P(Z > 0.38) = 1 - P(Z < 0.38) = 1 - 0.6480 = 0.3520

Option-E) none of the above

e) P(1 < Z < 1.5) = P(Z < 1.5) - P(Z < 1) = 0.9332 - 0.8413 = 0.0919

Option-D) 0.0919

f) P(Z < -0.38) = 0.3520

Option-D) 0.3520

g) P(Z < 1.38) = 0.9162

Option-C) 0.9162