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Assume that a typical computer manufactured by a company lasts 10 Months and that the standard deviation is 50 days. Computer life follows a normal distribution. What is the probability that a computer made by this company will last at most 1 Year?

Assumption is that one month has 30 days.

Can you please explain how this is calculated ?

Thanks

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  • $\begingroup$ Welcome to the site. This looks like a homework problem. If that is the case, please add the "self-study" tag. $\endgroup$ – Peter Flom - Reinstate Monica Oct 23 '13 at 10:10
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    $\begingroup$ For several hundred more questions like this, please search our site. $\endgroup$ – whuber Oct 23 '13 at 14:02
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Normal distribution has 2 parameters: mean and variance (or standard deviation which is the square root of variance).

Mean=10months*30days/month= 300 days

Therefore, lifetime, T, is distributed as Normal(mean=300 days, std. dev=50 days).

You want to find P(T< 365 days)
Calculate the z-score for T=365--> z = (365-300)/50=1.3
And use a table or software to find the appropriate cumulative ("lower tail") probability corresponding to z=1.3

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