Question

A lecture Hall has 200 seats with folding arm tablets, 30 of which are designed for left-handers. The average size of classes that meet there is 190, and we can assume that about 14% 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? (round to 4 decimal places)

0.0642

0.0838

0.2174

0.2557

0

Answer 1

P(left handed), p = 0.14

q = 1 - 0.14 = 0.86

Sample size, n = 190

Normal approximation to binomial: P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = np

= 190 x 0.14

= 26.6

Standard deviation =

=

= 4.783

Number of chairs for right handers = 170

P(a right-handed student in one of these classes is forced to use a lefty arm-tablet) = P(number of right handed people is 170 or more)

= P(number of left handed people is less than 20)

= P(X < 20)

= P(Z < (19.5 - 26.6)/4.783) (with continuity correction)

= P(Z < -1.484)

= 0.0689

Ans: 0.0642

Note: The slight difference must be because of some sounding errors