Question

The height of the students in a certain class is following normal distribution with mean

height as 165 cm and standard deviation of 25 cm. There are 60 students in that class.

Determine

i. The number of students whose height is more than 158 cm

ii. The number of students whose height is lying between 155 and 172 cm.

3. b. Find the lowest height among the tallest 5 student in a class.

Answer 1

$i) Given \; that, μ=165, σ=25, n=60,$

$P(x>158)=P(Z> 25 158−165 ​ ) =P(Z>−0.28)=0.5+P(0<Z<0.28)$

=0.5+0.1103

= 0.6103

$numberofstudents=60×0.6103=36.63≈37$

$ii)P(155<x<172)$

$=P(( \frac {155−165}{25} ​ )<Z< ( \frac {155−165}{25}))$

$=P(−0.4<Z<0.28)$

$=P(0<Z<0.4)+P(0<Z<0.28)$

$=0.1554+0.1103=0.2657$

number of students=60×0.2657=15.94≈16

b)Let it be 60 students in a class, so 5 tallest students is 5/60=8.3% in a class;

$P(x>X)=1-P(x<X)=0.083$

P(x<X)=1-0.083=0.917, using table, z-value for it equals 1.39

$(X-μ)/σ =1.39$

(x-165)/25=1.39,

x=165+25*1.39=199.75.

So, the lowest height among the tallest 5 students in a class equals 200cm.