Question

A coin is tossed 50 times. Find the probability that the tail appears.

A) Exactly  30 times

B at least 35 times.

Using normal distribution

Answer 1

X ~ Bin (n , p )

Where n = 50 , p = 0.50

Mean = n p = 50 * 0.5 = 25

Standard deviation = sqrt [ n p ( 1 - p) ] = sqrt [ 50 * 0.5 * 0.5 ] = 3.5355

Using normal approximation

P(X < x) = P(Z < ( x - mean) / SD )

a)

With continuity correction,

P(X = 30) = P(29.5 < X < 30.5)

=  P ( 29.5 < X < 30.5 ) = P ( Z < ( 30.5 - 25 ) / 3.5355 ) - P ( Z < ( 29.5 - 25 ) / 3.5355 )

= P ( Z < 1.56) - P ( Z < 1.27 )

= 0.9406 - 0.898 (From Z table)

= 0.0427

b)

With continuity correction,

P(X >= 35) = P(X > 34.5)

=  P ( X > 34.5 ) = P(Z > (34.5 - 25 ) / 3.5355 )

= P ( Z > 2.69 )

= 1 - P ( Z < 2.69 )

= 1 - 0.9964 (From Z table)

= 0.0036