If Z is Standard Normal Variable, answer the following questions. Please show you complete work for...

If Z is Standard Normal Variable, answer the following questions. Please show you complete work for each question.

a. What is the Z value if the area under the curve and to the right of Z is 0.95

b. What is the probability of Z is within the interval of -1.75 and 2.61?

c. What are the middle Z values (-Z and + Z) such that the area under the probability curve from -Z to +Z is 0.97?

Solutions

Expert Solution

(a) If Area to the right is 0.95, then area to the left is 0.05, i.e P(X < x) = 0.05

The Z value at this probability = -1.645

__________________________

(b) The probability = P(Z = 2.61) - P(Z = -1.75)

The probability at Z = 2.61 is = 0.9955 and The probability at Z = -1.75 is = 0.0401

Therefore the required probability = 0.9955 - 0.0401 = 0.9554

___________________________

Therefore 2*P(Z) = 1.97

P(Z) = 1.97 / 2 = 0.985

The z value at p = 0.985 is 2.17

Therefore the middle values are Z = -2.17 and Z = +2.17

_______________________________

orchestra answered 1 year ago

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