Using the binomial distribution, it is found that there is a 0.38 = 38% theoretical probability that all 6 bulbs will last for 4 months.
What is the binomial distribution formula?
The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem, we have that:
- There are 6 bulbs, hence n = 6.
- Each bulb has a 0.85 chance of lasting for at least 4 months, hence p = 0.85.
The probability that all 6 bulbs will last for 4 months is P(X = 6), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 6) = C_{6,6}.(0.85)^{6}.(0.15)^{0} \approx 0.38[/tex]
More can be learned about the binomial distribution at https://brainly.com/question/24863377
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