1) If the probability of a machine producing a defective part is 0.05, what is the probability of
finding exactly 5 defective parts from a sample of 100? (Assume that the process follows a
binomial distribution and round answer to four place
Answers
Given: The probability of a machine producing a defective part is 0.05.
To find: The probability of finding exactly 5 defective parts from a sample of 100.
Solution:
- Now we have given that probability of a machine producing a defective part is 0.05, so p = 0.05.
- Sample given is 100, so n = 100
- The probability to find be x = 5.
- So, the formula for binomial distribution will be:
P(x) = { n! / x!(n - x)! } × p^x × q^(n-x)
- So now putting the values in the formula, we get:
P(x) = { 100! / 5!(95)! } × 0.05^5 × 95^(95)
- So after solving this, the answer of P(X=x) comes out to be 0.1800
Answer:
So the probability of finding exactly 5 defective parts from a sample of 100 is 0.1800
Given : probability of a machine producing a defective part is 0.05 . process follows a binomial distribution
To find : probability of finding exactly 5 defective parts from a sample of 100
Solution:
probability of a machine producing a defective part is 0.05,
=> p = 0.05
q = 1 - p = 1 - 0.05 = 0.95
n = 100
P(x) = ⁿCₓ pˣqⁿ⁻ˣ
x = 5
P(5) = ¹⁰⁰C₅(0.05)⁵(0.95)⁹⁵
=> P(5) = 0.1800178
= 0.1800
0.1800 is the probability of finding exactly 5 defective parts from a sample of 100
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