Question

1. If the height of adults in Illinois State University can be modelled using H~ N(174,35.7). Where the height is measured in centimeters

a. What type of data is this? (4 points)

b. What is the probability that a randomly selected adult from the University has height between 166 and 183? (14 points, show your work)

Answer 1

Solution

(a) This is a normal distributed continuous data since the height data falls in a constant sequence.

(b) Probability that $166<Z<183$

Population mean $\mu =174$

Standard deviation $\sigma =35.7$

$Z=\dfrac{X-\mu}{\sigma}$

$P(\frac{166-174}{35.7}<Z<\frac{183-174}{35.7})$

$P(-0.224<Z<0.252)$

$=P(Z<0.252)-P(Z<-1.5)$

$=0.5995-0.4114$

$=0.1881$