a) P( Z > -0.45) = 1 - P( Z <= -0.45)
= 1 - 0.3264
= 0.6736
b) P( Z < 2.10 ) = 0.9821
c) P( 0 < Z < 2.10) = P( Z < 2.10) - P( Z < 0)
= 0.9821 - 0.5000
= 0.4821
d) P( -0.45 < Z < 2.10 ) = P( Z < 2.10) - P( Z < -0.45)
= 0.9821 - 0.3264
= 0.6558
(All values are obtained from normal distribution Z - table)
2. Calculate the probability from the z-table. a. P(Z > -0.45) b. P(Z < 2.10) c....
4. Let Z ~ N(0,1) be a standard normal variable. Calculate the probability (a) P(1 <Z < 2). (b) P(-0.25 < < < 0.8). (c) P(Z = 0). (d) P(Z > -1).
For a standard normal probability distribution, find the following a) P(z<1.2) b) P(z<−0.45) c)P(−0.4<z<1.8)
If n 5 and x 0.45, what is the probability of the following? (a) (b) (c) (d) X= 4 Xs3 X<2 X>1 (a) P(X- 4)= (Round to four decimal places as needed.)
1. Find the value of * that yields the probability shown a. P(Z <**)-0.0075 b. P(Z <=*) -0.9850 C. P(Z >z*) - 0.8907 d. P(Z >»*) -0.0110 For #1: a) P(Z < z*) = 0.0075 b) P(Z <z*) = 0.9850 c) P(Z > z*) = 0.8997 d) P(Z > z*) = 0.0110
IS Find the following probability for the standard normal random variable z. a. P(z<-1.02) b. P(z <2.03) c. P(0.68 szs2.03) d. P(-2.66szs1.56) a. P(z -1.02)(Round to four decimal places as needed.) b. Pize 2.03)=[] (Round to four decimal places as needed.) ook c. P(0.68 szs2.03) (Round to four decimal places as needed.) d.P(-2.66 s zs 1.56) = [□ (Round to four decimal places as needed.)
Probability 5. The discrete random variable Z has the following probability distribution 2 0.2 4 P(Z) 0.1 0.25 0.05 0.3 Which of the following is FALSE? A) P(Z < 2) 0.55 B) P(Z 2 4)- 0.45 C) P(Z 4)=0.9 D) P(Z3)-0.05 6. A random sample of 100 first-year students was selected to determine the average GPA they achieved at a university. A 95% confidence interval for the average GPA of the first-year students was 5.2 < H < 6.8 based...
Problem 4. Let the random variable Z have the probability density function 4 Z(2)- 0, otherwise (a) Calculate EIZ) (b) Calculate P(0 〈 Z 〈 1/2). (c) Calculate P(Z 〈 1/2 | Z > 0).ן (d) Calculate all the moments EZnj, for n 1,2,3, Your answer will be a formula that contains n.
Find: P(-2.36 < Z < -1.04 ) using the standard normal distribution table. O a. 1401 b..0717 C..1583 d. 9066 e. 8417 Of..0934
(4) Given Z N(0, 1) find the following: (a) P(Z 2 1.4) (b) P(Z> 0.75) (c) P(IZI S 2) (d) P(IZ 2 2) (e) Find z such that P(Z < z) = 0.11 (f) Find z such that P(Z > z) = 0.02
Find the indicated probability using the standard normal distribution. P(z>2.73) dard normal table