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

(i) $0.358$ (ii) $0.760$ (iii) $0.354$; $0.384$

Linear Combinations, Parameter Estimation, and Applied Probabilistic Modeling

Linear Combinations, Parameter Estimation, and Applied Probabilistic Modeling