Answer to Question #174972 in Statistics and Probability for Angel Dhian L. Rabacal

Question

Five hundred children participated in a field demonstration. Their heights averaged is 110 cm with a standard deviation of 6 cm. What is the probability that the height of a child, picked at random, is greater than 104 cm?

Answer 1

Here the everage heights of the $500$ children is $110$ cm with standard deviation $6$ cm.

Let $X$ be a random variable denotes the height of the students.

Then $X$ is normally distributed with mean $110$ cm and standard deviation $6$ cm.

Therefore we have $\mu =110$ and $\sigma=6$ .

Let us take $Z= \frac{X-\mu}{\sigma}$ . Then $Z=\frac{X-110}{6}$.

Now we have to find $P(X>104).$

$\therefore P(X>104)=P(Z>\frac{104-110}{6})$

$=P(Z>-1)$

$=0.5+P(0\leq Z\leq 1)$

$=0.5+0.3413$ [ from normal distribution table ]

$=0.8413$

Which is the required probability.