John joined a gym for 6 months. He pays 20$ per month plus a membership fee. If his bill is 150$, what was the membership fee?
2 answers:
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Answer:
(a) P(X = 18) = 0.25
(b) P(X > 18) = 0.53
(c) P(X ≤ 18) = 0.47
(d) Mean = 19.76
(e) Variance = 22.2824
(f) Standard deviation = 4.7204
Step-by-step explanation:
We are given that discrete random variable X has the following probability distribution:
X P (x) X * P(x)
* P(x)
13 0.22 2.86 169 37.18
18 0.25 4.5 324 81
20 0.20 4 400 80
24 0.17 4.08 576 97.92
27 0.16 4.32 729 116.64
(a) P ( X = 18) = P(x) corresponding to X = 18 i.e. 0.25
Therefore, P(X = 18) = 0.25
(b) P(X > 18) = 1 - P(X = 18) - P(X = 13) = 1 - 0.25 - 0.22 = 0.53
(c) P(X <= 18) = P(X = 13) + P(X = 18) = 0.22 + 0.25 = 0.47
(d) Mean of X, = ∑X * P(x) ÷ ∑P(x) = (2.86 + 4.5 + 4 + 4.08 + 4.32) ÷ 1
= 19.76
(e) Variance of X, = ∑
* P(x) -
= 412.74 - = 22.2824
(f) Standard deviation of X, =
=
= 4.7204 .