Question

A. Calculate the probability that a randomly selected z-score is less than 1.56. (Round to four decimal places.)

B. Calculate the probability that a randomly selected z-score is greater than 2.38. (Round to four decimal places.)

C. Calculate the probability that a randomly selected z-score is less than -0.76. (Round to four decimal places.)

D.Calculate the probability that a randomly selected z-score is greater than -1.11. (Round to four decimal places.)

E. Calculate the probability that a randomly selected z-score is between 1.34 and 2.18. (Round to four decimal places.)

F. Calculate the probability that a randomly selected z-score is between -2.00 and 2.00. (Round to four decimal places.)

G. Find the z-score of the 75th percentile. (Round to two decimal places.)

Answer 1

(A) z = 1.56

P(z<1.56) = NORMSDIST(1.56)

P(z<1.56) = 0.9406

(B) z = 2.38

P(z>2.38) = 1- NORMSDIST(2.38)

P(z>2.38) = 1 - 0.9913

P(z>2.38) = 0.0087

(C) z = -0.76

P(z<-0.76) = NORMSDIST(-0.76)

P(z<-0.76) = 0.2236

(D) z = -1.11

P(z>-1.11) = 1- NORMSDIST(-1.11)

P(z>-1.11) = 1 - 0.1335

P(z>-1.11) = 0.8665

(E) Between z = 1.34 and 2.18

P(1.34<z<2.18) = NORMSDIST(2.18)-NORMSDIST(1.34)

P(1.34<z<2.18) = 0.9854 - 0.9099

P(1.34<z<2.18) = 0.0755

(F) Between z = -2.00 and 2.0

P(-2<z<2) = NORMSDIST(2.00)-NORMSDIST(-2.00)

P(-2<z<2) = 0.9772-0.0228

P(-2<z<2) = 0.9545

(G) use excel function NORMSINV(area)

set area = 75/100 = 0.75

we get

75th percentile z score = NORMSINV(0.75) = 0.67