Question

The mean height of 385 students is 163 cm,the standard deviation is 10 cm. Assuming that the heights are normally distributed,what percent of the height are greater than 170 cm and how many students having a height between 155 cm and 165 cm?

Answer 1

Given :

mean height of students ($\mu$ ) = 163 cm

standard deviation ($\sigma$ ) = 10 cm

no.of students (n) = 385

i.) percent of height greater than 170 cm

=> p(x>170) = p(z > $\frac{x-\mu}{\sigma}$ )

= p(z > $\frac{170-163}{10}$ )

= p(z > 0.7)

= 0.242

= 24.2 %

ii.) no.of students having height between 155 cm and 165 cm

=> p(155 < x < 165) = p( $\frac{155-163}{10} < x < \frac{165-163}{10}$ )

= p( -0.8 < x < 0.2)

= 0.3674

$\therefore$ no.of students = 0.3674 * n

= 0.3674 * 385

= 141.5

$\approx$ 142