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 $.

1. Detemine two simulatneous linear equations satisfied by $\mu $ and $\sigma $.
2. 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)(i) $\mu-0.524400512\ldots\sigma=62$, $\mu+0.674489750\ldots\sigma=98$. (a)(ii) $\mu\approx77.7$ kg, $\sigma\approx30.0$ kg. (b) $0.229$ (c) $0.178$ (d) $0.808$, under the independent-occupant sampling model.

Linear Combinations, Probability Modeling, and Parameter Estimation

Linear Combinations, Probability Modeling, and Parameter Estimation

Solution:

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