Normal Distribution and Sampling Distribution The UB Bee Her

Normal Distribution and Sampling Distribution

The UB Bee Herald production department has embarked on a quality improvement effort. Its first project relates to the quality of the newspaper print. Each day, a determination needs to be made concerning how the newspaper is printed in terms of blackness, contrast, and sharpness. The overall rating of the print is measured on a standard scale in which the target value is 10.0. Data collected over the past year indicate that the overall rating is approximately normally distributed, with a mean of 10.5 and a standard deviation of 1.25. Each day, one page on the first newspaper printed is chosen, and the overall rating is measured. The printing of the newspaper is considered acceptable if the rating of the page is greater than 9.

(5 points) Assuming that the distribution has no changed from what it was in the past year, what is the probability that the overall rating is below 9?

(5 points) Above what overall rating 99% of the one page printing fall?

(5 points) If production takes a random sample of 5 pages on the first print run, what is the probability that the mean overall rating is below 9?

(5 points) Explain the difference in the probabilities calculated in (h) and (j).

Solution

Normal Distribution and Sampling Distribution

The UB Bee Herald production department has embarked on a quality improvement effort. Its first project relates to the quality of the newspaper print. Each day, a determination needs to be made concerning how the newspaper is printed in terms of blackness, contrast, and sharpness. The overall rating of the print is measured on a standard scale in which the target value is 10.0. Data collected over the past year indicate that the overall rating is approximately normally distributed, with a mean of 10.5 and a standard deviation of 1.25. Each day, one page on the first newspaper printed is chosen, and the overall rating is measured. The printing of the newspaper is considered acceptable if the rating of the page is greater than 9.

(5 points) Assuming that the distribution has no changed from what it was in the past year, what is the probability that the overall rating is below 9?

mean of 10.5 and a standard deviation of 1.25

z value for 9, z = (9-10.5)/1.25 = -1.2

P( x<9) = P( z < -1.2) = 0.1151

(5 points) Above what overall rating 99% of the one page printing fall?

Z value of 99% = -2.326

Required rating = 10.5-2.326*1.25 = 7.5925

(5 points) If production takes a random sample of 5 pages on the first print run, what is the probability that the mean overall rating is below 9?

n=5

standard error =1.25/sqrt(5) =0.559

z value for 9, z = (9-10.5)/0.559 = -2.68

P( mean x < 9) = P( z < -2.68) = 0.0037

(5 points) Explain the difference in the probabilities calculated in (h) and (j).

First one probability of less than a particular value and the second is probability of less than average of 5 sample values.