ECON106 HW5 1 Textbook questions, #s: 15.60 14.13, 14.14, 14.52a-c, 14.56, 15.49

Question

ECON106 HW5 1 Textbook questions, #s: 15.60 14.13, 14.14, 14.52a-c, 14.56, 15.49, 15.50, 2 Standard Normal CDF F(Z) 1.0000 0.6103 0.2327- -3 Using the CDF of a standard normal variable (Z) above, find the values for: a) b) d) what is the probability that a randomly selected z falls between a) and c)? e) The probability is that a randomly selected z falls between 0 and b). f) What is the estimated average height of the PDF for this distributino between -2.99 and -3.00? (you don't have to be very exact, but you should explain). g) What is the average height of the PDF between Z-0 and Z-b)? (to 4 decimal places)

Explanation / Answer

2a)

Here we need z-score , a, such that

P(Z < a ) = 0.2327

From z table the requried score is

a = -0.73

(b)

Here we need z-score , b, such that

P(Z < b ) = 0.6103

From z table the requried score is

b = 0.28

c)

Here we need z-score , c, such that

P(Z < c ) = 0.9382

From z table the requried score is

c = 1.54

d)

The required probability is : 0.9382 - 0.2327 = 0.7055

e)

Since area left to z-score 0 is 0.5 so the required probability is 0.6103 - 0.5 = 0.1103

f)

Here you need to find the probability

P(-3.00 < Z < -2.99)

So

P(-3.00 < Z < -2.99) = P(Z < -2.99) - P(Z < -3.00)

It is approximatley zero.

g)

It is 0.1103, from part e.

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