A basketball player claims to make 47% of her shots from the field. We want to simulate the player taking sets of 10 shots, assuming that her claim is true. Suppose this player attempts 10 shots in a...

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A basketball player claims to make 47% of her shots from the field. We want to simulate the player taking sets of 10 shots, assuming that her claim is true.

Suppose this player attempts 10 shots in a game and only makes 3 of them. Does this provide convincing evidence that she is less than a 47% shooter?

(a) Yes, because 3/10 (30%) is less than 47%.

(b) Yes, because she never made 47% of her shots in the simulation.

(d) No, because the simulation was only repeated 25 times.

(e) No, because the distribution is approximately symmetric.

Answered Same DayDec 25, 2021

Answer To: A basketball player claims to make 47% of her shots from the field. We want to simulate the player...

David answered on Dec 25 2021

110 Votes

Let us calculate the probability of getting such a low score.
P (X ≤ 3), n = 10, p = 0.47
P (X ≤ 3) = P (0 ≤ X ≤ 3) = P (X = 0, 1, 2, 3)
= P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3) (because these are disjoint
events)
P (X = 0) =
(10
0
)
(0.47)0(1 − 0.47)10 = 1(0.47)0(0.53)10 ≈ 0.001749
P (X = 1) =
(10
1
)
(0.47)1(1 − 0.47)9 = 10(0.47)1(0.53)9 ≈ 0.015509
P (X = 2)...

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A basketball player claims to make 47% of her shots from the field. We want to simulate the player taking sets of 10 shots, assuming that her claim is true. Suppose this player attempts 10 shots in a...

Answer To: A basketball player claims to make 47% of her shots from the field. We want to simulate the player...

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