Question

The heights of male students are normally distributed with a mean of 158 cm and a

standard deviation of 5 cm.


Find the percentage of male students who are between 145 cm and 170 cm.


Round your

answers to the nearest hundredths.

Answer 1

Answer: The percentage of male students who are between 145 cm and 170 cm = 98.71%

Explanation:

Let x denotes the height of male students.

As per given,

`\mu=158,\sigma=5`

The probability of male students who are between 145 cm and 170 cm

=
`P(145<X<170)`

`=P((145-158)/(5)<(X-\mu)/(\sigma)<(170-158)/(5))\\\\=P(-2.6<Z<2.4)\\\\=P(Z<2.4)-P(Z<-2.6)\\\\=P(Z<2.4)-(1-P(2.6))\\\\=0.9918-(1-0.9953)\\\\= $$0.9871`

Hence, the percentage of male students who are between 145 cm and 170 cm = 98.71%