Question

what is the expected value of the binomial distribution where n=16 and p=0.85 . (a) 6 (b) 7.5 (c) 12.5 (d) 13.6​

Answer 1

Answer:

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Answer 2

Answer:

Concept:

Binomial Distribution The binomial distribution formula is for any random variable X, given by;  

$P(x: n, p)={ }^{n} C_{x} p^{x}(1-p)^{n-x} \text { Or } P(x: n, p)={ }^{n} C_{x} p^{x}(q)^{n-x}$

where,

n = the number of experiments

x = 0, 1, 2, 3, 4, …

p = Probability of success in a single experiment

q = Probability of failure in a single experiment (= 1 – p)

Step-by-step explanation:

Given:

n = 16

p = 0.85

Find:

expected value of the binomial distribution

Solution:

q = 1 - p = 1 - 0.85 = 0.15

The Binomial distribution is given by

$P(X=r)={ }^{16} C_{r}(0.85)^{r} \times(0.15)^{16-r}$

The expected value

= E(X)

= np

= 16 × 0.85

= 13.6

The expected value of the binomial distribution is 13.6  i.e., option (d)

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