Alice and Bertha are playing around on the court, shooting baskets. Alice claims

Question

Alice and Bertha are playing around on the court, shooting baskets. Alice claims that she can score from the foul line 80% of the time. Bertha scoffs at her saying that even LeBron has a lower success rate than that. She claims that Alice has very little skill and whether she makes a basket or not is random (that is, she scores half the time). Bertha proposes a test: Alice should shoot from the foul line ten times. If she lands the ball through the basket at least 8times, Bertha will believe that Alice’s success rate is greater than 50%. If not, Bertha’s opinion will be unchanged. Let the probability that Alice scores from the foul line be denoted by p.

If the null hypothesis is true, then the distribution (i.e. binomial, hypergeometric, ect.) of the number of baskets that Alice makes is (include n, p, and or r) :

If the null hypothesis is true, then the chance that Alice will score at least 8 baskets is closest to:

Explanation / Answer

The Null hypothesis is that Alice's success rate is 50% ,i.e., p=0.5.

The distribution of the number of baskets is a binomial distribution with p = 0.5

The distribution is given as: C [n, r] X (pr) X (1-p)n-r, where C[] represents the combination.

The chance that Alice will score at least 8 out of 10 baskets =

C[10,8] x (0.5)8 x (0.5)2 + C[10,9]x(0.5)9 x (0.5)1 + C [10,10]x(0.5)10 x (0.5)0 = 0.043945+0.009766+0.000977 =0.054688

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