A survey is conducted in a large office building. It is found that $30%$ of the office workers wei

Question

A survey is conducted in a large office building. It is found that $30%$ of the office workers weigh less than $62$ kg and that $25\%$ of the office workers weigh more than $98$ kg. The weights of the office workers may be modelled by a normal distribution with mean $\mu $ and standard deviation $\sigma $. Detemine two simulatneous linear equations satisfied by $\mu $ and $\sigma $. Find the values of $\mu $ and $\sigma $.[6] Find the probability that an office worker weighs more than $100$ kg. [1] There are elevators in the office building that take the office workers to their offices. Given that there are $10$ workers in a particular elevator, find the probability that at least four of the workers weigh more than $100$ kg. [2] Given that there are $10$ workers in an elevator and at least one weight more than $100$ kg, find the probability that there are fewer than four workers exceeding $100$ kg. [3]

Accepted Answer

(a)(ii) $\mu =77.7$, $\sigma =30.0$ (b) $0.229$ (c) $0.178$ (d) $0.808$

Linear Combinations, Probability Modeling, and Parameter Estimation

Linear Combinations, Probability Modeling, and Parameter Estimation