Question

a normal population has a mean u=120 and a standard deviation of o=10. That is, X~N (120,10)

please help me answer the following questions using this data.

1)What is the zscore for an individual value of 133?

2) What is the probability that a randomly chosen individual from this population will be greater than 112? (report to four decimal places)

3) what is the probability that a randomly chosen individual from this population will be between 117 and 131?

4) if samples of size 25 are drawn from the population, what is the mean of the sampling distribution of X?

5) if samples of size 25 are drawn from the population, what is the standard deviation of the sampling distribution of X?

6) what is the probability that the sample mean from a sample of size 25 will be less than 116?

thank you very much

Answer 1

1) z-score = (x - )/

                = (133 - 120)/10 = 1.3

2) P(X > 112)

= P((X - )/ > (112 - )/)

= P(Z > (112 - 120)/10)

= P(Z > -0.8)

= 1 - P(Z < -0.8)

= 1 - 0.2119

= 0.7881

3) P(117 < X < 131)

= P((117 - )/ < (X - )/ < (131 - )/)

= P((117 - 120)/10 < Z < (131 - 120)/10)

= P(-0.3 < Z < 1.1)

= P(Z < 1.1) - P(Z < -0.3)

= 0.8643 - 0.3821

= 0.4822

4) = 120

5) = = 10/ = 2

6) P( < 116)

= P(( - )/() < (116 - )/())

= P(Z < (116 - 120)/2)

= P(Z < -2)

= 0.0228