a)
Here, n = 4, p = 0.1, (1 - p) = 0.9 and x = 1
As per binomial distribution formula P(X = x) = nCx * p^x * (1 -
p)^(n - x)
We need to calculate P(X <= 1).
P(X <= 1) = (4C0 * 0.1^0 * 0.9^4) + (4C1 * 0.1^1 * 0.9^3)
P(X <= 1) = 0.6561 + 0.2916
P(X <= 1) = 0.9477
b)
Here, n = 6, p = 0.1, (1 - p) = 0.9 and x = 1
As per binomial distribution formula P(X = x) = nCx * p^x * (1 -
p)^(n - x)
We need to calculate P(X > 1).
P(X <= 1) = (6C0 * 0.1^0 * 0.9^6) + (6C1 * 0.1^1 * 0.9^5)
P(X <= 1) = 0.5314 + 0.3543
P(X <= 1) = 0.8857
P(x > 1) =1- 0.8857
= 0.1143
c)
Here, n = 6, p = 0.3, (1 - p) = 0.7 and x = 3
As per binomial distribution formula P(X = x) = nCx * p^x * (1 -
p)^(n - x)
We need to calculate P(X < 3).
P(X < 3) = (6C0 * 0.3^0 * 0.7^6) + (6C1 * 0.3^1 * 0.7^5) + (6C2
* 0.3^2 * 0.7^4)
P(X < 3) = 0.1176 + 0.3025 + 0.3241
P(X < 3) = 0.7442
d)
Here, n = 3, p = 0.4, (1 - p) = 0.6 and x = 2
As per binomial distribution formula P(X = x) = nCx * p^x * (1 -
p)^(n - x)
We need to calculate P(X >= 2).
P(X >= 2) = (3C2 * 0.4^2 * 0.6^1) + (3C3 * 0.4^3 * 0.6^0)
P(X >= 2) = 0.288 + 0.064
P(X >= 2) = 0.3520
(1 point) If X is a binomial random variable, compute the probabilities for each of the...
(1 point) If X is a binomial random variable, compute the probabilities for each of the following cases: (a) P(X < 1), n = 7, p = 0.3 Probability = (b) P(X > 5), n = 7, p = 0.1 Probability = (C) P(X < 6), n = 8, p = 0.5 Probability = (d) P(X > 2), n = 3, p = 0.5 Probability =
(1 point) If X is a binomial random variable, compute the probabilities for each of the following cases: (a) P(X < 2), n = 9, p = 0.4 Probability = (b) P(X > 3), n = 8, p = 0.35 Probability = (c) P(X < 2), n = 5, p = 0.1 Probability = (d) P(X 25), n = 9, p = 0.5 Probability =
(1 point) If X is a binomial random variable, compute the probabilities for each of the following cases: (a) P(X < 3), n = 9, p = 0.3 Probability = (b) P(X > 4), n = 5, p = 0.3 Probability = (c) P(X<5), n = 7.p = 0.35 Probability = (d) P(X > 6), n = 7, p = 0.3 Probability =
(1 point) If z is a binomial random variable, compute P(C) for each of the following cases: (a) Px <6), n=8, p = 0.3 P(x) = (b) P(x > 2), n = 3, p=0.5 P(x) = (c) Pa<5), n = 8, p=0.6 P(x) = (d) P(x > 2), n = 3, p = 0.7 P(x) =
(1 point) If X is a binomial random variable, compute P(X = x) for each of the following cases: (a) n = 4, p = 0.1, x = 1 P(X = x) (b) n=6, p = 0.3.x = 3 P(X = x) (c) n= 3, p = 0.4, x = 1 P(X = x) (d) n = 3, p = 0.15, x = 2 P(X = x)
7. If x is a binomial random variable find the following probabilities: a) P(x = 2) n = 10 and p = .40 b) P (x < 5) for n = 15 and p = .60 8. Find pl, oland o for n = 25 and p = .50
2. Suppose you have a random variable X distributed as N(2,6). Compute the following probabilities b) P(X<2) c) P(1 X<2) d) P(IX-21 <2)
5. Imagine a random variable X that has a binomial distribution with n = 12 and p = 0.4. Determine the following probabilities a) P(X 5) b) P(X s2) c) P(X9) d) P (3 X<5)
2. Suppose you have a random variable X distributed as N(2,6). Compute the following probabilities. b) P(X<2) c) P(1<X<2)
If x is a binomial random variable, use the binomial probability table to find the probabilities below. a.. P(x=2) for n=10, p=0.4 b.. P(x≤6) for n=15, p=0.3 c.. P(x>1) for n=5, p=0.1 d.. P(x<17) for n=25, p=0.9 e.. P(x≥6) for n=20, p=0.6 f.f. P(x=2) for n=20, p=0.2 a. P(x=2)=_______________-(Round to three decimal places as needed.)