The Probability of Computers Not Crashing in a Day

What is the probability that at least 95 out of 158 computers will not crash in a day?

a) 0.9997 b) 0.0003 c) 0.9993 d) None

Answer:

The probability that at least 95 out of 158 computers will not crash in a day is approximately 0.9997.

To find the probability that at least 95 out of 158 computers will not crash in a day, we can use the binomial distribution. The probability that a given computer will not crash in a day is 64%, which corresponds to a success probability of 0.64. The formula for the probability of at least a certain number of successes is given by the cumulative distribution function (CDF) for the binomial distribution.

Using this formula, we can calculate the probability of at least 95 successful outcomes out of 158 trials. The answer is approximately 0.9997.