Problem 7 Consider the normal distribution N( = 57, = 9). (a) Find the lower qua

Question

Problem 7 Consider the normal distribution N( = 57, = 9). (a) Find the lower quartile 1 (b) Find the upper quartile Q3. (c) Find the interquartile range (IQR). (d) Find the area to the left of Q1 1.5 IQR. (e) Find the area to the right of Q3 1.5 IQR. (f Suppose you have a data set with 1000 values that can be approximated by the normal distribution with = 36.7 and = 0.4. How many values do you expect to be outside of the interval (01 1.5 IQR, Q3 +1.5 IQR)? (g) Generate 1000 random values of the normal distribution N( = 57, = 9) and store them in the variable x as follows: set.seed(2202) x-rnorm(1 Now create a boxplot and count the number of outliers. How many did you count? 000, mean-57, sd-9)

Explanation / Answer

a) Q1 = -0.67449*9+57 = 50.93 ( rounded to two decimal places)

b) Q3 = 0.67449*9+57 = 63.07 ( rounded to two decimal places)

c) IQR = Q3-Q1 = 63.07-50.93 = 12.14

d) Q1-1.5IQR = 50.93-1.5*12.14 = 32.72

P(x<32.72)

= P(z<(32.72-57)/9)

= 0.0035

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