Question

A lecture hall has 150 seats with folding arm tablets, 24 of which are designed for left-handers. The typical size of classes that meet there is 144 , and we can assume that about 18% of students are left-handed. Assuming that all students sit in the correct left- or right-handed desk if one is available, use a Normal approximation to find the probability that a right-handed student in one of these classes is forced to use a lefty arm tablet. The probability that a right-handed student in one of these classes is forced to use a lefty arm tablet is (Type an integer or decimal rounded to three decimal places as needed.)

Answer 1

Using the Normal approximation to the binomial distribution, it's found that there are enough desks for right-handers such that the probability of a right-handed student having to use a left-handed desk is 0.

Step-by-step explanation:

To find the probability that a right-handed student is forced to use a left-handed desk, we can use the Normal approximation to the binomial distribution. We have 150 seats with 24 designed for left-handers. Since the class size is 144 and 18% are left-handed, we expect 144 * 18% = 25.92 left-handed students, rounded to approximately 26 students.

Because the number of seats for left-handers is less than the expected number of left-handed students, we can assume all lefty desks will be taken by left-handed students. This leaves 150 - 24 = 126 seats for right-handers and 144 - 26 = 118 right-handed students. The excess number of right-handers without a desk is thus 118 - 126 = -8, which means that every right-handed student will have a seat designed for them. In this scenario, it's not possible for any right-handed student to be forced to use a lefty desk, so the probability is 0.