The normal distribution

load("more/bdims.RData")

mdims <- subset(bdims, sex == 1)
fdims <- subset(bdims, sex == 0)

hist(mdims$hgt, main = "Men's Heights", xlab = "Height")

hist(fdims$hgt, main = "Women's Heights", xlab = "Height")

The distribution’s shape is unimodal on both histograms. Hovewer men’s histogram looks more normal.

Data follows a nearly normal distribution, because it’s unimodal and bell-shaped.

Not all of the points fall on the line towards the tail. But area within standart diviation shows more normality.

fhgtmean <- mean(fdims$hgt)
fhgtsd   <- sd(fdims$hgt)
sim_norm <- rnorm(n = length(fdims$hgt), mean = fhgtmean, sd = fhgtsd)
qqnorm(sim_norm)
qqline(sim_norm)

Probability plot for fdims$hgt look similar to the plots created for the simulated data. It can provide evidence that female heights are normal.

It is a normal distribution, however there is a lot of outliers on the right tail.

qqnormsim(fdims$wgt)

hist(fdims$wgt, probability = TRUE)

What is the probability that a randomly chosen young adult female is shorter than 160 cm?

pnorm(q = 160, mean = fhgtmean, sd = fhgtsd)

## [1] 0.2282939

What is the probability that a randomly chosen young adult female has weight more than 55 kg?

sum(fdims$wgt > 55) / length(fdims$wgt)

## [1] 0.6923077

It is right skewed.

On Your Own

1

a-B;

b-C;

c-D;

d-A.

2

Since age is whole number it might cause stepwise pattern.

3

It is right skewed.

qqnorm(fdims$kne.di)
qqline(fdims$kne.di)

hist(fdims$kne.di, main = "Women's Knee", xlab = "Knee Diameter")