(11) a) Suppose the life of a particular brand ofcalculator battery is normally

Question

(11) a) Suppose the life of a particular brand ofcalculator battery is normally distributed with amean of 75 hours and a standard deviation of 10 hours. If asingle battery is randomly selected from the population,use Table 4 (Standard Normal probability table), software, or theTI-83/84 to find the probability that its life will be less than 80hours.   

(11) b) Suppose the life of a particular brand of calculatorbattery is normally distributed with a mean of 75 hours and astandard deviation of 10 hours. If 16 batteriesare randomly selected from the population, use Table 4 (StandardNormal probability table), software, or the TI-83/84 to find theprobability that the sample mean life will be between 70 and 80hours. Use the Central LimitTheorem.

Explanation / Answer

(11) a) mean , =75 hours

standard deviation, = 10 hours.

If a single battery is randomly selected fromthe population, the probability that its life will be lessthan 80 hours i.e P(X<80)

=P(Z<(X-)/)=P(Z<(80-75)/10 ) =P(Z<0.5) =0.6915

(11) b) mean, = 75 hours

standard deviation , = 10 hours.

if 16 batteries are used, standard error, e = / n= 10/16 = 2.5

P(X<70)

=P(Z<(X-)/e)=P(Z<(70-75)/2.5 ) =P(Z<-2) = 0.0228

P(X<80)

=P(Z<(X-)/e)=P(Z<(80-75)/2.5 ) =P(Z<2) =0.9772

If 16 batteries are randomly selected from thepopulation, the probability that the sample mean life will bebetween 70 and 80 hours = 0.9544

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