Answer:
0.99804932311
Step-by-step explanation:
We solve this using binomial probability
Binomial probability formula
= nCx × p^x × q^n - x
= n!/(n - x)! x!
Where n = Number of trials = 25 samples
x = Number of successes = 23
p = probability of success = 99% = 0.99
q = probability of failure = 1 - p
= 1 - 0.99
= 0.01
Hence,
p(at least 23 are properly filled) = p(X ≥ x)
= [25!/(25 - 23)! × 23! × 0.99^23 × 0.01^25 - 23 ]+ [25!/(25 - 24)! × 24! × 0.99^24 × 0.01^25 - 24 ]+ [25!/(25 - 25)! × 23! × 0.99^25 × 0.01^25 - 25]
= [300 × 0.99 ^23 × 0.01^2] + [25 × 0.99^24 × 0.01^1] + [1 × 0.99^25 + 0.01^0]
= 0.0238084285 + 0.1964195352 + 0.7778213594
= 0.99804932311
