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Chapter 17: Problem 31

A lecture hall has 200 seats with folding arm tablets, 30 of which are designed for left-handers. The typical size of classes that meet there is 188, and we can assume that about \(13 \%\) of students are left-handed. What's the probability that a right-handed student in one of these classes is forced to use a lefty arm tablet?

Short Answer

Expert verified
0 probability; right-handed students won't need left-handed seats.

Step by step solution

01

Determine the Number of Left-handed Seats

The lecture hall has a total of 200 seats, out of which 30 are designed for left-handed students. These are the special left-handed seats available.
02

Calculate Expected Number of Left-handed Students

The class size is 188 students, and 13% of them are left-handed. The number of left-handed students can be calculated as follows: \(0.13 \times 188 = 24.44\). Since the number of students must be whole, we round it to 24 left-handed students.
03

Evaluate Left-handed Seat Occupancy

We have 30 left-handed seats and approximately 24 left-handed students. Since 24 left-handed students will occupy 24 of the 30 left-handed seats, there will still be 6 left-handed seats remaining.
04

Determine Available Right-handed Seats

Out of the 200 total seats, 170 are for right-handed students (200 total seats - 30 left-handed seats). Since 24 left-handed students occupy left-handed seats, 164 seats remain available for right-handed students.
05

Calculate Probability of Right-handed Using Lefty Tablet

There are 188 total students and 24 are left-handed, leaving 164 right-handed students. Since there are 164 right-handed seats (with 6 unoccupied left-handed seats still available), all right-handed students will get a right-handed seat without occupying a left-handed seat. Hence, the probability is \(0\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Right-handed Students
In most environments, right-handed students make up the majority of the class. This is important because seating arrangements often cater primarily to them. Let鈥檚 look closer at how right-handedness affects seat selection in a lecture hall.
  • Right-handed seats are typically designed with arm tablets on the right side. This is to accommodate the ease of writing for right-handed individuals.
  • In our example, of the 200 total seats, there are 170 designed for these students.
  • Given that right-handed students derive from the remaining 87% of the class, it鈥檚 crucial to ensure they have adequate seating options.
Understanding the proportion of right-handed students ensures there are enough seats for everyone and helps planners avoid uncomfortable situations, like having right-handed students forced to use left-handed arm tablets. In the exercise scenario, with all measures correctly in place, right-handed students end up using right-handed seats without any issue.
Left-handed Students
Left-handed students often face unique challenges in lecture halls due to the limited number of specially designed seats. Here, let鈥檚 explore more about the accommodations required for left-handed students.
  • Lecture halls should include left-handed seating, typically featuring an arm tablet on the left side. This is crucial for the students鈥� comfort and effectiveness in writing.
  • In the given problem, out of 200 sets, 30 are specifically designed for left-handed students, which is roughly 15% of all seats.
  • The exercise tells us approximately 13% of a class, or about 24 students, are left-handed, indicating an adequate number of dedicated seats.
Properly accommodating left-handed students means providing sufficient seating that meets their needs. In our example, the planning leaves 6 left-handed seats unoccupied, offering an excellent balance for these students, preventing any necessity for right-handers to use these seats.
Lecture Hall Seating Arrangement
Seating arrangements in a lecture hall are pivotal for accommodating the various needs of students. Good planning takes into account the proportions of right-handed versus left-handed students.
  • Understanding the composition of a class helps assign the right mix of seating after considering statistical or historical data, such as the percentage of left-handed and right-handed individuals.
  • The efficient arrangement of seats ensures students are comfortable and not forced into unsuitable seating, potentially affecting their ability to focus and work.
  • In the scenario from the exercise, the seating plan provided is near-perfect, with plenty of right-handed seats available for all the right-handed students and an excess of left-handed seats for those students.
Seating arrangements that match student demographics ensure everyone has a seat that caters to their needs. Understanding probability and logistical constraints can help in designing these arrangements more effectively, as seen with zero probability of right-handed students having to use left-handed seats in this well-planned example.

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Most popular questions from this chapter

A basketball player who ordinarily makes about \(55 \%\) of his free throw shots has made 4 in a row. Is this evidence that he has a "hot hand" tonight? That is, is this streak so unusual that it means the probability he makes a shot must have changed? Explain.

A wildlife biologist examines frogs for a genetic trait he suspects may be linked to sensitivity to industrial toxins in the environment. Previous research had established that this trait is usually found in 1 of every 8 frogs. He collects and examines a dozen frogs. If the frequency of the trait has not changed, what's the probability he finds the trait in a) none of the 12 frogs? b) at least 2 frogs? c) 3 or 4 frogs? d) no more than 4 frogs?

Police estimate that \(80 \%\) of drivers now wear their seatbelts. They set up a safety roadblock, stopping cars to check for seatbelt use. a) How many cars do they expect to stop before finding a driver whose seatbelt is not buckled? b) What's the probability that the first unbelted driver is in the 6 th car stopped? c) What's the probability that the first 10 drivers are all wearing their seatbelts? d) If they stop 30 cars during the first hour, find the mean and standard deviation of the number of drivers expected to be wearing seatbelts. e) If they stop 120 cars during this safety check, what's the probability they find at least 20 drivers not wearing their seatbelts?

Assume that \(13 \%\) of people are left-handed. If we select 5 people at random, find the probability of each outcome described below. a) The first lefty is the fifth person chosen. b) There are some lefties among the 5 people. c) The first lefty is the second or third person. d) There are exactly 3 lefties in the group. e) There are at least 3 lefties in the group. f) There are no more than 3 lefties in the group.

Shortly after the introduction of the euro coin in Belgium, newspapers around the world published articles claiming the coin is biased. The stories were based on reports that someone had spun the coin 250 times and gotten 140 heads - that's \(56 \%\) heads. Do you think this is evidence that spinning a euro is unfair? Explain.
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