Step by step solution to "a) To calculate; the value of P(X=17) Given:..."

permaneceerc

Answered question

2021-09-20

a) To calculate; the value of

P (X = 17)

Given:

n = 20

p = 0.85

b) To calculate; the value of

P (X \leq 12)

Faiza Fuller

Skilled2021-09-21Added 108 answers

a) Explanation:
Definition Binomial Probability:

P (X = k) = (b e g \in {a r r a y} {c} n ∖ k e n d {a r r a y}) \times p^{k} \times {(1 - p)}^{n - k}

P (X = 17) = (b e g \in {a r r a y} {c} 20 ∖ 17 e n d {a r r a y}) \times {(0.85)}^{17} \times {(0.15)}^{20 - 17} \approx 0.2428 = 24.28 %

b) Explanation:
Definition Binomial Probability:

P (X = k) = (b e g \in {a r r a y} {c} n ∖ k e n d {a r r a y}) \times p^{k} \times {(1 - p)}^{n - k}

P (X \leq 12) = P (X = 0) + P (X = 1) + \dots + P (X = 12) \approx 0.0059 \approx 0.59 %

As the probability is a really small value, therefore the event is unlikely to happen by chance and therefore Judy must be suspicious.

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