Many people consider their smart phone to be essential! Communication, news, Internet, entertainment, photos, and just keeping current are all conveniently possible with a smart phone. However, the battery better be charged or the phone is useless. Battery life of course depends on the frequency, duration, and type of use. One study involving heavy use of the phones showed the mean of the battery life to be 9.75 hours with a standard deviation of 2.3 hours. Then the battery needs to be recharged. Assume the battery life between charges is normally distributed.
(a) Find the probability that with heavy use, the battery life
exceeds 10 hours. (Round your answer to four decimal places.)
(b) You are planning your recharging schedule so that the
probability your phone will die is no more than 5%. After how many
hours should you plan to recharge your phone? (Round your answer to
the nearest tenth of an hour.)
_ hours
Solution :
Given that ,
mean = = 9.75
standard deviation = = 2.3
(a)
P(x > 10) = 1 - P(x < 10)
= 1 - P[(x - ) / < (10 - 9.75) / 2.3)
= 1 - P(z < 0.11)
= 1 - 0.5438
= 0.4562
Probability = 0.4562
(b)
Using standard normal table ,
P(Z > z) = 5%
1 - P(Z < z) = 0.05
P(Z < z) = 1 - 0.05
P(Z < 1.65) = 0.95
z = 1.65
Using z-score formula,
x = z * +
x = 1.65 * 2.3 + 9.75 = 13.5
13.5 hours
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