SOLUTION: The life of an alkaline battery in constant use is a normally distributed random variable with mean 18 hours and standard deviation 2 hours. i) What is the probability that a batt

Algebra ->  Probability-and-statistics -> SOLUTION: The life of an alkaline battery in constant use is a normally distributed random variable with mean 18 hours and standard deviation 2 hours. i) What is the probability that a batt      Log On


   

Question 835719: The life of an alkaline battery in constant use is a normally distributed random variable with mean 18 hours and standard deviation 2 hours.
i) What is the probability that a battery tested at random lasts longer than 15 hours?
ii) Estimate how many batteries should be purchased to have 1000 those last at least 16 hours.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.z=%28x-m%29%2Fsigma=%2815-18%29%2F2=-3%2F2
P%28-3%2F2%29=0.0668
So the probability it lasts longer than 15 hours is,
P=1-0.0668=0.9332
.
.
.
2..z=%28x-m%29%2Fsigma=%2816-18%29%2F2=-2%2F2=1
P%28-1%29=0.158655
15.8655% would fail by 16 hours so 84.135% would survive.
1000%2FX=.84135
X=1188.573
You should buy 1189 batteries.