Question 359712
A car battery is known by the manufacturer to last 65 months with a standard deviation of 4.5 months.
a. If the manufacturer guarantees them for five years (60 months), what percentage of them will they have to replace?
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z(60) = (60-65)/4.5 = -1.1111
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%(x < 60) = P(z < -1.1111) = 13.33%
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b. If the manufacturer does not want to replace more than 4% of the batteries, for how many months should they guarantee them (round to the nearest whole month)?
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Find the z-value with a right tail of 4%.
invNorm(0.96) = 1.7507
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Find the corresponding raw score value:
x = zs+u
x = 1.7507*4.5+65
x = 72.88 months
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He should guarantee them for 72 months or 6 years.
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Cheers,
Stan H.