Please answer all parts with work! 2 Standard Normal CDF F(2) 1.0000 0.6103 - a)

Question

Please answer all parts with work!

2 Standard Normal CDF F(2) 1.0000 0.6103 - a) b)c 3 Z 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 f) What is the estimated average height of the PDF for this distributino between -2.99 and -3.00? (you that a randomly selected z falls between 0 and b) 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

Referring to standard normal table,

Note the values of Z corresponding to values of probabilities given in standard normal table

a)for P = 0.2327, Z = - 0.73

b) for P = 0.6103, Z = 0.28

c) for P = 0.9382, Z = 1.54

d)

P( Z falls between a and c) = P(c) - P(a)

= 0.9382 - 0.2327

= 0.7055

e)

P(Z falls between 0 to b) = P(b) = 0.6103

f)

average ht of PDF between -2.99 to -3.00

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

= 0.0014 - 0.0013 = 0.0001

g)

Avg height between Z=0 and Z=b

= P(Z=b) - P(Z=0)

= 0.6103-0.5

= 0.1103

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