Answer to Question #169793 in Statistics and Probability for Pauline Scarlet

Question

In a medical examination,300 people undergo a height measurement and was found out that the average height of all are 150 cm.

Answer 1

If the standard deviation is 19, find the number of people that fall under the given conditions:

a)with the height less than 132cm

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

where

Z=z-score

X=variable value

μ=mean

σ=standard deviation

Assuming normal distribution, the left-tail normal distribution table gives the probability of the z-score (or less).

(a)If N=300 and random sampling, we can assume normal distribution.

μ=150 cm

σ=19 cm

x=132

$Z=\dfrac{132-150}{19}=-0.9474$

P(X<132)=P(Z<-0.9474)=0.1717 (from left-tail normal probability tables)

$\Rightarrow$ approximate number of people with heights <132 = 0.1717*300=51.52=52 persons