A lecture hall has 250250 seats with folding arm tablets, 3030 of which are designed for left-handers. The typical size of classes that meet there is 230230, and we can assume that about 1515% of students are left-handed. 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 is nothing.

Question

contestada

Respuesta :

sammyayol2013 sammyayol2013 · Answer 1 · 2019-11-01T21:05:55+01:00

Answer: P=0

Step-by-step explanation:

Let X be a random variable that denotes the number of right handed students in the class.

X follows binomial distribution with n=230 and

p=1−0.15=0.85

Using Normal approximation to approximate the required binomial probability:

Mean, μ=np=230×0.85=195.5

Standard deviation, σ=√np(1−p)=√230×0.85(1−0.85)=5.42

Probability that a right-handed student in one of these classes is forced to use a left arm seat

We are given that 30 seats are designed for lefties, the rest of the 220 seats are for righties.

Incase there are more than 220 righties, then one or more righties are forced to use the left handed tablets.

Hence the required probability is;

P(X>220)=P((x−μ)/σ < (220.5−195.5)/5.42)

=P(Z>4.62)=1−P(Z<4.62). (Using standard normal distribution table)

P=1- 1= 0

P= 0