Question

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 =9​, p =0.8​, x ≤3
The probability of x ≤3 successes is ?. ​(Round to four decimal places as​ needed.)

Answer 1

Answer on Question #61152 – Math – Statistics and Probability

Question

A binomial probability experiment is conducted with the given parameters. Compute the probability of $x$ successes in the $n$ independent trials of the experiment.

$n = 9, p = 0.8, x \leq 3.$

The probability of $x \leq 3$ successes is ? (Round to four decimal places as needed.)

Solution

Given the binomial distribution with parameters $n = 9$, $p = 0.8$, $q = 1 - p = 0.2$,

$$P_n(k) = C_n^k p^k q^{n-k},$$

where $C_n^k = \frac{n!}{k!(n-k)!}$, $n! = 1 \cdot 2 \cdot 3 \cdot \ldots \cdot (n-1) \cdot n$.

Then the probability of $x \leq 3$ successes is

$$P(x \leq 3) = P_9(0) + P_9(1) + P_9(2) + P_9(3) = C_9^0 p^0 q^9 + C_9^1 p^1 q^8 + C_9^2 p^2 q^7 + C_9^3 p^3 q^6 = 0.0037.$$

Answer: 0.0037.

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