Question

In: Statistics and Probability

A lecture hall at NC State has 215 seats with fold-down writing pedestals, 25 of which...

A lecture hall at NC State has 215 seats with fold-down writing pedestals, 25 of which are designed for left-handers. An Intro. to Economics class with 215 students meets in this lecture hall. Assume that 13% of the general population is left-handed.

Question 1. 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?

(Use 4 decimal places.)

Question 2. 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?

(Use 3 decimal places.)

Expert Solution

Answer:

Given that:

A lecture hall at NC State has 215 seats with fold-down writing pedestals, 25 of which are designed for left-handers. An Intro. to Economics class with 215 students meets in this lecture hall. Assume that 13% of the general population is left-handed.

13% of the students are left handed and 100-13 = 87% are right handed

There are 215 sets.Of them,25 are designed for left handers and 215-25 = 190 for right handers

There are 215 students,so n= 215

1) 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?

In this case a success is a student being right handed.So the probability of success is p=0.87

There are 190 seats for right handed students.If there are 191 or more right handed students,they will have to use a seat designed for a left hander. We have to find P(X>190).The probability can be obtained as

²¹⁵C₁₉₀²¹⁵C₂₁₅

The required probability is 0.2461

2) 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?

There are 25 seats for left handed students.If there are 26 or more,at least one is going to be forced to use a seat designed for a right hander

In this case, a success is a student being left handed. So the probability of success is p=0.13. We have to find P(X>25)

The probability can be obtained as

²¹⁵C₁₉₀²¹⁵C₂₁₅

Thus,the required probability is 0.6835

orchestra answered 1 year ago

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