Question

16. You will flip a fair coin 200 times. What is the approximate probability you will get at least 53% Heads?
(A) 0.8485 (B) 0.1711 (C) 0.8023 (D) 0.1977 (E) 0.1515

Answer 1

Solution:

Given:  a fair coin is flipped 200 times. Thus n = 200 and p = probability of head = 0.5

We have to find the  approximate probability you will get at least 53% Heads.

That is we have to find:

Plp > 0.53) = ....

Find z score:

р-р Грх(1-р)

2 = 0.53 -0.5 0.5x(1-0.5) 200

0.03 0.5x0.5 200

0.03 0.00125

0.03 0.035355

=0.85

Thus we get:

P p > 0.53) = P(Z > 0.85)

P p > 0.53) = 1- P(Z < 0.85)

Look in z table for z = 0.8 and 0.05 and find area.

「 | 0.0 lol 10.2 10.3 10.4 10.5 10.6 |o.7 10.8 .00 .01 .02 .03 .04 1.05 - 106 5000 5040 .5080 .5120 5160 499 5239 5398 .5438 54785517 155575 96 15636 .5793 1.5832 .5871 .5910 .5948 87 .6026 .6179 .6217 .6255 .6293 .6331 .6168 .6406 .6554 .6591 16628 .6664 .6700 .66.672 .6915 .6950 .6985 .7019 7054 08 7123 .7257.72917324.73577389742.7454 580 7611 7642 7673 ,704 7764 764 79217010703070677005-18023 ,8051 .07 5279 ,5675 .6064 .6443 ,6808 7157 1.7486 794 .8078 .08 5319 5714 .6103 ,6480 .684 7190 7517 7823 .8106 .09 5359 15753 .6141 .6517 .6879 7224 .7549 7852 8133

P( Z < 0.85) =0.8023

Thus

P p > 0.53) = 1- P(Z < 0.85)

P p > 0.53) = 1 - 0.8023

P p > 0.53) = 0.1977

Thus  the approximate probability you will get at least 53% Heads is 0.1977

Answer 2

Solution:

Given:  a fair coin is flipped 200 times. Thus n = 200 and p = probability of head = 0.5

We have to find the  approximate probability you will get at least 53% Heads.

That is we have to find:

Plp > 0.53) = ....

Find z score:

р-р Грх(1-р)

2 = 0.53 -0.5 0.5x(1-0.5) 200

0.03 0.5x0.5 200

0.03 0.00125

0.03 0.035355

=0.85

Thus we get:

P p > 0.53) = P(Z > 0.85)

P p > 0.53) = 1- P(Z < 0.85)

Look in z table for z = 0.8 and 0.05 and find area.

「 | 0.0 lol 10.2 10.3 10.4 10.5 10.6 |o.7 10.8 .00 .01 .02 .03 .04 1.05 - 106 5000 5040 .5080 .5120 5160 499 5239 5398 .5438 54785517 155575 96 15636 .5793 1.5832 .5871 .5910 .5948 87 .6026 .6179 .6217 .6255 .6293 .6331 .6168 .6406 .6554 .6591 16628 .6664 .6700 .66.672 .6915 .6950 .6985 .7019 7054 08 7123 .7257.72917324.73577389742.7454 580 7611 7642 7673 ,704 7764 764 79217010703070677005-18023 ,8051 .07 5279 ,5675 .6064 .6443 ,6808 7157 1.7486 794 .8078 .08 5319 5714 .6103 ,6480 .684 7190 7517 7823 .8106 .09 5359 15753 .6141 .6517 .6879 7224 .7549 7852 8133

P( Z < 0.85) =0.8023

Thus

P p > 0.53) = 1- P(Z < 0.85)

P p > 0.53) = 1 - 0.8023

P p > 0.53) = 0.1977

Thus  the approximate probability you will get at least 53% Heads is 0.1977

Answer 3

Solution:

Given:  a fair coin is flipped 200 times. Thus n = 200 and p = probability of head = 0.5

We have to find the  approximate probability you will get at least 53% Heads.

That is we have to find:

Plp > 0.53) = ....

Find z score:

р-р Грх(1-р)

2 = 0.53 -0.5 0.5x(1-0.5) 200

0.03 0.5x0.5 200

0.03 0.00125

0.03 0.035355

=0.85

Thus we get:

P p > 0.53) = P(Z > 0.85)

P p > 0.53) = 1- P(Z < 0.85)

Look in z table for z = 0.8 and 0.05 and find area.

「 | 0.0 lol 10.2 10.3 10.4 10.5 10.6 |o.7 10.8 .00 .01 .02 .03 .04 1.05 - 106 5000 5040 .5080 .5120 5160 499 5239 5398 .5438 54785517 155575 96 15636 .5793 1.5832 .5871 .5910 .5948 87 .6026 .6179 .6217 .6255 .6293 .6331 .6168 .6406 .6554 .6591 16628 .6664 .6700 .66.672 .6915 .6950 .6985 .7019 7054 08 7123 .7257.72917324.73577389742.7454 580 7611 7642 7673 ,704 7764 764 79217010703070677005-18023 ,8051 .07 5279 ,5675 .6064 .6443 ,6808 7157 1.7486 794 .8078 .08 5319 5714 .6103 ,6480 .684 7190 7517 7823 .8106 .09 5359 15753 .6141 .6517 .6879 7224 .7549 7852 8133

P( Z < 0.85) =0.8023

Thus

P p > 0.53) = 1- P(Z < 0.85)

P p > 0.53) = 1 - 0.8023

P p > 0.53) = 0.1977

Thus  the approximate probability you will get at least 53% Heads is 0.1977