Question

1 point) Suppose we will flip a fair coin 100 times. Let X be the number of heads, and use a Normal distribution to approximate the distribution of X. (a) Apply the continuity correction: P(42≤X≤58)= P( -8/5 0 )

Answer 1

Explanation:

When a fair coin is tossed 100 times X no of heads is binomial with n =100 and p = 0.50

Mean = np = 50 and Variance = npq = 25

so std dev = 5

When approximated to normal

X : no of heads : N(50,5)

Required probability

i)
`P(42≤X≤58)\\= P(41.5<X<58.5)`(applying continuity correction_

= F(58.5) -F(41.5)

= 0.9554-0.0446

=0.9108

ii)
`P(-8/5<X<8/5)\\= F(1.6) -F(-1.6)\\= 0.00000`

c)
`P(X\geq 50) = P(X\geq 49.5)\\= 1-F(49.5)\\= 0.5398`

d) P(X>0)

=1-0.0000

=1