1). Answer the Following Given Bellow. A). Let Z be a standard normal variable.

ID: 3350428 • Letter: 1

Question

1). Answer the Following Given Bellow.

A). Let Z be a standard normal variable. Find the value of z if z satisfies P(Z > z) = 0.6331.

a) -0.34

b) 0.34

c) 0.35

d) -0.30

e) 0.30

f) None of the above.

B). Let Z be a standard normal variable. Find the value of z if z satisfies P(Z < z) = 0.0052.

a) 0.05

b) -2.56

c) -1.50

d) -2.50

e) 2.55

f) None of the above.

C). Suppose X is a normal random variable with = 40 and = 20. Find P(X > -11.4).

a) 0.0051

b) 0.9949

c) 0.9938

d) 0.0062

e) 0.9867

f) None of the above.

A) The value can be found out from the standard normal distribution table

P(Z > z) = 0.6331

So, P(Z < z) = 1 - 0.6331 = 0.3669

Z = -0.34 (option a)

B) P(Z < z) = 0.0052

Z = -2.56 (option b)

c) P(X < A) = P(Z < (A - mean)/standard deviation

P(X > - 11.4) = 1 - P(X < -11.4)

= 1 - P(Z < (-11.4 - 40)/20)

= 1 - P(Z < -2.57)

= 1 - 0.0051

= 0.9949 (option b)

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