Question

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 15.25 hours with a standard deviation of 2.2 hours. Then the battery needs to be recharged. Assume the battery life between charges is normally distributed.

Required:
a. Find the probability that with heavy use, the battery life exceeds 11 hours.
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?

Answer 1

a) The probability that with heavy use, the battery life exceeds 11 hours is 0.4602.

b) Using the standard normal table, After 6.8 hours should you plan to recharge your phone.

Explanation:

a) The probability that with heavy use, the battery life exceeds 11 hours:-

P(x > 11) = 1 - p( x< 11)

`=1- p P[(x - \mu) / \sigma < (11 - 10.75) / 2.4]\\\\=1- P(z < 0.10)`

Using z table distribution,

= 1 - 0.5398

= 0.4602

b) Using the standard normal table,

`P(Z < z) = 5%\\\\\\\\= P(Z < -1.645 ) = 0.05 \\z = -1.645`

Using the z-score formula,

`x = z * \sigma + \mu\\x = -1.645 * 2.4 + 10.75\\x = 6.8 hours.`