Write a HW4.Rmd

Write a HW4.Rmd    

(Your Name Here)

    • 1 QQ plots ## 1a

## 1b ## 1c

    • 2 Fiber

    • 2a

    • 2b

# 3 Bulls

Knit your .Rmd    le to an .html    le along the way. Turn in the .html to Canvas.

1. For each of the three samples, make a normal QQ plot. Look at the QQ plot and say whether the data are plausibly from a normal population or whether they are evidence against a normal population. (Hint: In each case, to get some context for your decision, make a few QQ plots from samples of the same size that did come from a normal population. Please do not include these context plots in your submission.)

(a) data = c(7,13.2,8.1,8.2,6,9.5,9.4,8.7,9.8,10.9,8.4,7.4,8.4,10,9.7,8.6,12.4,10.7,11,9.4)

(b) data = c(2.5,1.8,2.6,-1.9,1.6,2.6,1.4,0.9,1.2,2.3,-1.5,1.5,2.5,2.9,-0.1)

(c) data = c(3.3,1.7,3.3,3.3,2.4,0.5,1.1,1.7,12,14.4,12.8,11.2,10.9,11.7,11.7,11.6)

2. A maker of dietary ber supplement tablets claims its bottles contain, on average, 250 g of the supplement, with a standard deviation of 2 g.

(a) Find the probability a randomly selected bottle weighs between 246 and 254 g. To do this, suppose the bottle weights are approximately normally distributed. Hint: Standardizing a random single weight requires subtracting its mean and dividing by its standard deviation .

(b) 100 bottles are selected randomly. Find the probability that their average weight is less than 250 g. Do

not assume any longer that the bottle weights are normally distributed. Hint: Standardizing a random p

sample mean weight requires subtracting its mean    and dividing by its standard deviation  =  n.

    3. The Hereford Cattle Society says that the mean weight of a one-year-old Hereford bull is 1135 pounds, with a standard deviation of 97 pounds. Suppose 40 bulls are randomly selected and loaded on a train car. Find the probability their combined weight exceeds 46000 pounds. (Hint: The combined weight exceeds 46000 pounds if the average weight exceeds 4600040 = 1150 pounds.)

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