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 200200 times and gotten 108108 headsminus−​that's 5454​% heads. a )font size decreased by 1a) Use the Normal model to approximate the Binomial to determine the probability of spinning a fair coin 200200 times and getting at least 108108 heads. b )font size decreased by 1b) 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

Answer:

(a) 0.12924

(b) Taking into consideration significance level of 0.05 yet the value of p is greater than 0.05, it suggests that the coin is fair hence the coin can be used at the beginning of any sport event.

Explanation:

(a)

n=200 for fair coin getting head, p= 0.5

Expectation = np =200*0.5=100

Variance = np(1 - p) = 100(1-0.5)=100*0.5=50

Standard deviation, $s = \sqrt {variance}=\sqrt {50}= 7.071068$

Z value for 108, $z =\frac {108-100}{7.071068}= 1.131371$

P( x ≥108) = P( z >1.13)= 0.12924

(b)

Taking into consideration significance level of 0.05 yet the value of p is greater than 0.05, it suggests that the coin is fair hence the coin can be used at the beginning of any sport event.