Question

The probability of a piece to live for at least 5 years is 0.8. Accordingly, 5 of these parts are used

a) Find the probability that 3 of them will fail before 5 years.

b) How many are expected to live longer than 5 years.

Answer 1

Solution:

a) Probability = 0.0512

b) Expected value = 4

Explanation:

Given that,

The probability of a piece to live for at least 5 years is 0.8.

i.e. p = 0.8

5 of these parts are used

Sample size , n = 5

By using binomial distribution,

a) The probability that 3 of them will fail before 5 years is given by,

probability of piece to live before 5 years = 1 -0.8 = 0.2

  

By using EXCEL------ BINOMDIST(3,5,0.2,0)

Probability = 0.0512

So, The probability that 3 of them will fail before 5 years is 0.0512

b) Expected to live longer than 5 years is given by,

i.e. Mean = np = 5(0.8) = 4

Expected to live longer than 5 years is 4

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