Replace Distress Flare: Normal Distribution Life with 90% and 99% Success Rates

[Sirsh]

3. A local manufacturer creates distress flares. The times the flares last are normally distributed with a mean life of 9.8 years and a standard deviation of 1.3 years.
(b) A small boat owner who regularly travels out to sea wants to be sure his distress flare works. Determine when he should replace the distress flare, given he wants a better than:
(i) 90% chance the flare will work
(ii) 99% chance the flare will work.

For this question i am not sure what to do.. I thought that if it had said works for.. 11years you'd do z = (11-9.8)/1.3 then use this value to find out the proability. but with the percentages i am unsure. Could some please help me! much apprechiated.! :_)

 

[hgfalling]

This is like the inverse of what you are describing. Suppose they had asked you "After 11 years, what is the probability that the flare is working?" And you would calculate your z-score (11-9.8)/1.3, look it up in a table, or use a computer, or whatever.

The question they are asking you now is, "After how many years will the probability of the flare working be below 90%?" This is a pretty similar problem; only now you're looking through your table at the probabilities and getting the z-scores instead of the other way around.

 

[Sirsh]

So would the probability of a certain flare be 0.9 then you'd have to find the z score, then put the z scores value into the equation z = (x-mean)/stnd dev and then you'd find the x value and that'd be the amount of years it would work for?

 

[HallsofIvy]

Yes!