Consider the probability that less than 13 out of 151 CDs will be defective. Assume the probability that a given CD will be defective is 12%
To calculate the probability that less than 13 out of 151 CDs will be defective, we can use the binomial probability formula.
The formula for the probability of getting exactly k successes in n trials with a probability of success p is given by:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
- P(X = k) is the probability of getting exactly k successes
- C(n, k) is the combination of n items taken k at a time
- p^k is the probability of k successes
- (1-p)^(n-k) is the probability of (n-k) failures
In this case, we want to find the probability that less than 13 out of 151 CDs are defective.
To do this, we need to calculate the cumulative probability for k = 0, 1, 2, ..., 12.
P(X < 13) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 12)
Let's calculate this probability step by step:
1. Calculate the probability of a CD being defective (p = 0.12).
2. Calculate the probability of a CD not being defective (1-p = 0.88).
3. Calculate the cumulative probability of less than 13 defective CDs using the binomial formula for each value of k from 0 to 12.
4. Sum up these probabilities to get the final result.
Alternatively, we can use statistical software or online calculators that can directly calculate the cumulative binomial probability for us.