Question

Marks for this submission: 7.00/7.00. Accounting for Consider the normal distribution N(u = 73, σ = 8). (a) Find the lower quartile Q1. 67.6x (b) Find the upper quartile Q3. 78.4x (c) Find the interquartile range (IQR), 10.8 (d) Find the area to the left of Q1-1.5-IQR. | .0038 (e) Find the area to the right of Qs +1.5. IQR. 9965 Suppose you have a data set with 1000 values that can be approximated by the normal distribution with μ = 36.7 and σ = i How many values do you expect to be outside of the interval (Q1-1.5-IQR, Q3 + 1.5 . IOR) 4 X (g) Generate 1 000 random values of the normal distribution N(μ 73, σ 8) and store them in the variable x as follows: set.seed(2540) x=rnorm (1000, means 73, sd-8) Now create a boxplot and count the number of outliers. How many did you count?3 Check You have correctly selected 2

Answer 1

We can simulate this in R as follows , The compelte R snippet is as follows

set.seed(123)

data <- rnorm(1000,mean=73,sd=8)

q <- quantile(data)

q

IQR = q[4] - q[2]
IQR

boxplot(data, horizontal = TRUE, axes = FALSE, staplewex = 1,col="steelblue")
text(x=fivenum(data), labels =round(fivenum(data),2), y=1.25)

The results are

> q
0% 25% 50% 75% 100%
50.52180 67.97341 73.07368 78.31681 98.92832
> IQR
75%
10.34341

50.52 67.97 73.07 78.32 98.93

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