The heights, in metres, of female and male students in a particular school follow normal distributio

Question

The heights, in metres, of female and male students in a particular school follow normal distributions with the following data.

	Mean Height (metres)	Variance (metres$^{2}$)
Female	$1.6$	$0.04$
Male	$\mu $	${{\sigma }^{2}}$

It is known that $20\%$ of the males are shorter than $1.6$ m, while $75\%$ of them are below $1.8$ m. Show that $\mu $ and $\sigma $ are $1.71$ m and $0.132$ m respectively.

Find the probability that

The heights of two randomly selected female students both exceed $1.55$ m.[2]
The total height of two randomly selected female students is more than $3$ m. [3]
A randomly selected male student is taller than a randomly selected female student by at least $20$ cm.[3]

A random sample of $20$ female students is chosen. Find the probability that at least $15$ of these female students are shorter than $1.7$ m.[4]

Accepted Answer

$\mu\approx1.71$ m, $\sigma\approx0.132$ m (shown). (i) $0.358$ (ii) $0.760$ (iii) $0.355$ using unrounded parameters; $0.354$ using the displayed rounded parameters. Final sample probability: $0.384$.

	Mean Height (metres)	Variance (metres\(^{2}\))
Female	\(1.6\)	\(0.04\)
Male	\(\mu \)	\({{\sigma }^{2}}\)

Linear Combinations, Parameter Estimation, and Applied Probabilistic Modeling

Linear Combinations, Parameter Estimation, and Applied Probabilistic Modeling

Solution:

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