Question

Four hundred draws are made at random with replacement from a box of numbered tickets; 195 are positive. Someone tells you that 50% of the tickets in the box show positive numbers. Do you believe it? Answer yes or no, and explain.

Answer 1

Yes

Number of tickets, n = 400

P( a ticket is positive), p = 0.5

q = 1 - p = 0.5

If 50% of tickets are positive, mean number of positive tickets = np

= 400 x 0.5

= 200

Standard deviation =

=

= 10

If a value is within 2 standard deviations of mean, it can be considered as a usual event. Here, the range of number of tickets that can be considered casual = 200 2x10 = 180 to 220

Number of positive tickets = 195, which is within the usual range. So, we can believe the claim that 50% of the tickets in the box show positive numbers.