Question

A lecture hall has

200200

seats with folding arm​ tablets,

1818

of which are designed for​ left-handers. The typical size of classes that meet there is

188188​,

and we can assume that about

1212​%

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.

​(Type an integer or decimal rounded to four decimal places as​ needed.)

Answer 1

total seats=200

number of left hands seats=18

number of right handed seats=182

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a typical class size = 188

P(left handed) = 0.12

P(right handed) = 1 - 0.12 = 0.88

maximum right handed students of a class can have 182 .if the right handed students are more than this, then they are forced to sit on left handed chair.

mean = n p = 188*0.88 = 165.44

std dev = √(np(1-p)) = √(188*0.12*0.88) = 4.4556

np≥10 and n(1-p)≥10 ,so binomial distribution can be approximated to normal distribution.

without continuity correction

P(X≥183 ) = P(Z > (x-µ)/σ ) = P(Z> (183-165.44)/4.4556) = P(Z>3.941) = P(Z<-3.941) = 0.000041

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with continuity correction factor

P(X ≥183) = P(Xnormal ≥182.5)

  

Z=(Xnormal - µ ) / σ = 3.828848153

  

=P(Z ≥3.828848153) = 0.0001