Percentage of a normal population above a value, both of two independent items within an interval, and a value from a percentage below it
Percentage of a normal population above a value, both of two independent items within an interval, and a value from a percentage below it
8 marks
The length of time, \(X\) hours, for which the battery of a particular model of phone lasts on a full charge is normally distributed with mean \(18\) hours and standard deviation \(2.5\) hours.
- Find the percentage of these batteries that last for more than \(20\) hours.
- Two of these batteries are chosen at random. Find the probability that each of the two lasts for between \(15\) hours and \(19\) hours.
- It is known that \(88.49\%\) of these batteries last for less than \(h\) hours. Find the value of \(h\).
[8]
Solution:
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Answer:(a) \(21.2\%\) (b) \(0.292\) (c) \(h=21.0\)
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