Question

A binomial probability experiment is conducted with the given parameters. Use technology to find the probability of X successes in the n independent trials of the experiment.

n=9, p=0.25, x<4

P(x<4)=

A binomial probability experiment is conducted with the given parameters. compute the probability of X successes in the n independent trials of the experiment.

n=10, p=0.6, x=5

P(5)=

Answer 1

a)

Here, n = 9, p = 0.25, (1 - p) = 0.75 and x = 4
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X < 4).
P(X < 4) = (9C0 * 0.25^0 * 0.75^9) + (9C1 * 0.25^1 * 0.75^8) + (9C2 * 0.25^2 * 0.75^7) + (9C3 * 0.25^3 * 0.75^6)
P(X < 4) = 0.0751 + 0.2253 + 0.3003 + 0.2336
P(X < 4) = 0.8343

b)

Here, n = 10, p = 0.6, (1 - p) = 0.4 and x = 5
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 5)
P(X = 5) = 10C5 * 0.6^5 * 0.4^5
P(X = 5) = 0.2007
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