Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

Let X ~ Normal (=3, 2 =16) and Z ~ Normal (0,1) use the Standard Normal Table in

ID: 3340592 • Letter: L

Question

Let X ~ Normal (=3, 2=16) and Z ~ Normal (0,1) use the Standard Normal Table in Appendix B or MS Excel to find each of the following:

a. P(Z = 1)

b. P(Z < 0)

c. P(Z 1)

d. P(|Z| < 1)

e. P(|Z| > 1.5)

f. P(|Z| > 2)

g. P(0.5 < Z < 1)

h. The point z such that P(Z z)=0.8

i. The point z such that P(Z z)=0.8

j. The point z such that P(-z Z z)=0.9

k. P(X = 1)

l. P(X < 0)

m. P(X 1)

n. P(|X| < 1)

o. P(|X| > 1.5)

p. P(|X| > 2)

q. P(0.5 < X < 1)

r. P(- < X < +)

s. P(- 2 < X < +2)

t. The point x such that P(X x)=0.8

Problem(1) Let X ~ Normal( = 3, 2 = 16) and Z ~ Normal (0, 1), use the Standard Normal Table in Appendix B or MS Excel to find each of the following: (a) P(Z = 1) (b) P(Z 2) (g) P(0.5

Explanation / Answer

Solution- Z follows normal ( 0,1 )

(a) P(Z=1)

= 0 [ As in continous probability distribution, probability at a point is zero]

(b) P(z< 0)

= 0.5

(c) P( Z < 1)

= 0.8413

(d) P( |Z| < 1 )

= P( -1 < Z < 1)

= 0.6826

(e) P( |Z| > 1.5 )

= P( Z > 1.5) + P( Z < -1.5 )

= .066 +.066

= 0.133

(f) P( |Z| > 2 )

= P( Z > 2) + P( Z < -2 )

= 0.22 + 0.22

= 0.0455

Answers

TY!