Given that z is a standard normal random variable, find z for each situation. (Round your answers to two decimal places.) (a) The area to the right of z is 0.08. (b) The area to the right of z is 0.025. (c) The area to the right of z is 0.05. (d) The area to the right of z is 0.10.

Given that,

a)

P(z > z) = 0.08

1 - P (z  < z) = 0.08

P   (z  < z) = 1 - 0.08) = 0.92

P (z  < 1.41) = 0.92

z = 1.41

b)

P(z > z) = 0.025

1 - P (z  < z) = 0.025

P   (z  < z) = 1 - 0.025) = 0.975

P (z  < 1.96) = 0.975

z = 1.96

c)

P(z > z) = 0.05

1 - P (z  < z) = 0.05

P   (z  < z) = 1 - 0.05) = 0.95

P (z  < 1.65) = 0.95

z = 1.65

d)

P(z > z) = 0.10

1 - P (z  < z) = 0.10

P   (z  < z) = 1 - 0.10) = 0.9

P (z  < 1.28) = 0.9

z = 1.28

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47