Question

A lecture hall has 100 seats with folding arm tables, 12 of which are designed for left handers. The typical size of classes that meet there is 93, and we can assume that about 15% 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 table

The probability is:

(Round to four decimal places as needed)

Answer 1

Result:

A lecture hall has 100 seats with folding arm tables, 12 of which are designed for left handers. The typical size of classes that meet there is 93, and we can assume that about 15% 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 table

The probability is:

(Round to four decimal places as needed)

88 tablets are for righties
12 tablets are for lefties

Class size is 93
Average number of lefties is 0.15*93 = 13.95
Average number of righties is 0.85*93 = 79.05

If there are 89 or more righties in the class, then a righty will need to take on the wrong table.

Probability of righty is 085
Number of trials is 93
Number of successes is 89

we have to find P( x >= 89 )

Expectation = np = 79.05

Variance = np(1 - p) = 11.8575

Standard deviation = 3.4435

With continuity correction, z value for 89, z =(88.5-79.05)/3.4435 =2.74

P( x >=89) = P( z > 2.74)

=0.0031