A lecture hall at NC State has 220 seats with fold-down writing pedestals, 25 of

Question

A lecture hall at NC State has 220 seats with fold-down writing pedestals, 25 of which are designed for left-handers. An Intro. to Economics class with 213 students meets in this lecture hall. Assume that 13% of the general population is left-handed.

What is the probability that at least one right-handed student in this class is forced to use a seat designed for a left-hander?

What is the probability that at least one left-handed student in this class is forced to use a seat designed for a right-hander?

Explanation / Answer

The probability that a student is right or left handed can be considered as a binomial distribution.

1) Answer is 0.01467

Let p = 0.87 be the probaility success(a student being right handed).

There are 213 students each of them having a 87% probability of being right handed.

Thus n=213,

x= number of success required = 195.

If more than 195 students are right handed then at least 1 will be forced to use seat designed for left handed.

Binomial(195, 213, 0.87, true) in excel gives the cumulative probability value = 0.98533

Therefore the probability that right handed student will be forced to use a seat meant for left handed is 1-0.98533 = 0.01467

2) Answer is 0.6648

Using similar argument for left handed students, we need to find the parameter,

1 - Binomial(25, 213, 0.13, true) = 1- 0.3352 = 0.6648.

That is we need to find the probability that there are more than 25 success in 213 trials with each trial having 13% prrobability.

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