Question

Consider the probability that at least 96 out of 152 computers will not crash in a day. Assume the probability that a given computer will not crash in a day is 66%.Approximate the probability using the normal distribution. Round your answer to four decimal places.

Answer 1

0.2061

Explanation:

Probability (no crash) = 66% = 0.66

Average (no crash) expected out of 152 computers = 0.66 (152) = 100.32

Standard deviation 's' = √ [ (154) (0.66) (1-0.66) ] = √ (154) (0.66) (0.34)

= √ 34.5576 = 5.87

P (x > 96) = 1 - P (x < 95)

z= (x - u) / s ; x = sample mean = 95.5 (continuity correction factor = 0.5) , u = population average = 100.32

z = (95.5 - 100.32) / 5.87 = 4.82 / 5.87 = 0.82

P (x < 95) = P (z < 0.82) = 0.7939

P (x > 96) = 1 - 0.7939 = 0.2061