Question

For Questions 6 - 8, let the random variable X follow a Normal distribution with variance σ² = 625.

Q6. A random sample of n = 50 is obtained with a sample mean, X-Bar of 180.

What is the probability that population mean μ is greater than 190?

a. What is Z-Score for μ greater than 190 ==>

b. P[Z > Z-Score] ==>

Q7. What is the probability that μ is between 198 and 211?

a. What is Z-Score1 for μ greater than 198 ==>

b. What is Z-Score2 for μ less than 211 ==>

c. P[Z-Score1 < Z < Z-Score2] ==>

Q8. A second random sample of n = 75 is obtained, again with a sample mean X-Bar of 180. What is the probability that μ is between 177 and 190?

a. What is Z-Score1 for μ greater than 177 ==>

b. What is Z-Score2 for μ less than 190 ==>

c. P[Z-Score1 < Z < Z-Score2] ==>

Answer 1

6)

a)
mean = 180 . s = 625 , n =50

P(x > 190) = P(z > (190 -180)/(625/sqrt(50))
= P(z > 0.1131)
= 0.4550

7)

a)

P(z> 198) = P(z >(198 - 180)/(625/sqrt(50))
= 0.2036

P(x< 211) = P( z < (211 - 180)/(625/sqrt(50))
= 0.3507

P(198 < x < 211)
= P((198 - 180)/(625/sqrt(50)) < z < (211 - 180)/(625/sqrt(50))

= P(0.2036 < z < 0.3507)
= 0.0564

8)

n = 75

P(177 < x <190)

P(z> 177) = P(z >(177- 180)/(625/sqrt(50))
= -0.0339

P(x< 190) = P( z < (190 - 180)/(625/sqrt(50))
= 0.1131

P(- 0.0339 < z < 0.1131)

= 0.0585