Question

Shortly after the introduction of a new​ coin, newspapers published articles claiming the coin is biased. The stories were based on reports that someone had spun the coin 150 times and gotten 90 headsminus​that's 60​% heads.

a) right parenthesis font size decreased by 1 Use the Normal model to approximate the Binomial to determine the probability of spinning a fair coin 150 times and getting at least 90 heads.

b) right parenthesis font size decreased by 1 Do you think this is evidence that spinning this new coin is​ unfair? Would you be willing to use it at the beginning of a sports​ event? Explain.

Answer 1

(a)

n = 150

If it fair coin: p = 0.5

q = 1 - p = 0.5

Mean = = np = 150 X 0.5 = 75

SD =

To find P(X90):

Applying Continuity Correction, we get:

To find P(X > 89.5):

Z = (89.5 - 75)/6.1237

= 2.37

Table gives area = 0.4911

So,

P(X > 89.5) = 0.5 - 0.4911 = 0.0089

So,

The probability of spinning a fair coin 150 times and getting at least 90 heads = 0.0089

So,

Answer is:

0.0089

(b)

This is evidence that spinning this new coin is​ unfair. We would not be willing to use it at the beginning of a sports​ event because Z score = 2.37 > 2, So, it is an unusual event.