Question

# A: Let z be a random variable with a standard normal distribution. Find the indicated probability....

A: Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)
P(z ≤ 1.11) =

B: Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)

P(z ≥ −1.24) =

C: Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)

P(−1.78 ≤ z ≤ −1.14) =

D: Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 40; σ = 16

P(50 ≤ x ≤ 70) =

E: Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 97; σ = 12

P(x ≥ 90) =

We need to use standard normal z table to solve this problem

A)

From z table, P(z<1.11) = 0.8665

B)

From z table, P(z>-1.24) = 0.8925

C)

P(-1.78<z<-1.14) = p(z<-1.14) - p(z<-1.78)

P(z<-1.14) = 0.1271

P(z<-1.78) = 0.0375

So answer is 0.1271 - 0.0375 = 0.0896

D)

As the data is normally distributed we can use standard normal z table to estimate the answers

Z = (x-mean)/s.d

Given mean = 40

S.d = 16

P(50 < x< 70)

P(x<70)

Z = (70-40)/16 = 1.88

From z table, P(z<1.88) = 0.9699

P(x<50)

Z = (50 - 40)/16 = 0.63

From z table, P(z<0.63) = 0.7357

Required probability is 0.9699 - 0.7357 = 0.2342

E)

P(x>90)

Z = (90 - 97)/12 = -0.58

From.z.table, P(z>-0.58) = 0.7190

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