4.59 Space shuttle failures. Prior to the grounding of space shuttle program, th

Question

4.59 Space shuttle failures. Prior to the grounding of space shuttle program, the National Aeronautics and Space Ad ministration (NASA) estimated that the chance of a "crit cal-item" failure within a space shuttle's main engine was approximately 1 in 63. The failure of a critical item during flight would lead directly to a shuttle catastrophe. a. On average, how many shuttle missions would fly be- fore a critical-item failure occurs? sions before a critical-item failure occurs? sions before a critical-item failure occurs with proba- b. What is the standard deviation of the number of mis- C. Give an interval that will capture the number of mis- bility of approximately .95.

Explanation / Answer

this follows geometric distribution with paramter p=1/63

a) average number of suttle missions before a critical item failure =1/p-1=1/(1/63)-1=62

b)

standard deviaiton =sqrt((1-p)/p2)=62.498

c)

her let number of missions =x

P(X<=x)=0.95

1-(1-1/63)x =0.95

(62/63)x =0.05

solving above x =187.23

henec interval is from x=0 to 187

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