Question

A coin is tossed 1,000 times. What is the chance that the number of heads will be between 495 to 505?

Answer 1

Number of tosses, n = 1000

P(Head), p = 0.5

q = 1 - 0.5 = 0.5

P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = np

= 1000 x 0.5

= 500

Standard deviation =

=

= 15.81

P(number of heads will be between 495 to 505) = P(495 X 505)

= P(X < 505.5) - P(X < 494.5)   (with continuity correction)

= P(Z < (505.5 - 500)/15.81) - P(Z < (494.5 - 500)/15.81)

= P(Z < 0.35) - P(Z < -0.35)

= 0.6368 - 0.3632

= 0.2736