Find P(x \leq 1 | n = 15

Efan Halliday

Efan Halliday

Answered question

2021-09-21

Find P(x1n=15,p=0.25) by using the binomial formula.

Answer & Explanation

i1ziZ

i1ziZ

Skilled2021-09-22Added 92 answers

Step 1
Solution: We are given that a random variable x follows the binomial distribution with n=15 and p=0.25.
Therefore, we are given:
n=15,p=0.25
Step 2
We have to find:
P(x1)
Step 3
Now using the binomial probability mass function, we have:
P(X=x)=n!(nx)!x!px(1p)nx
Therefore, we have:
P(x1)=P(x=0)+P(x=1)
=15!(150)!0!0.250(10.25)150+15!(151)!1!0.251(10.25)151
=(1×1×0.013363)+(15×0.25×0.017818)
=0.013363+0.066817
=0.0802
Step 4
Therefore, we have:
P(x1)n=15,p=0.25)=0.0802

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