Average talk time between charges of a cell phone battery is advertised as 3.6 h

Question

Average talk time between charges of a cell phone battery is advertised as 3.6 hours. Assume that talk time/battery life is normally distributed with a standard deviation of 0.8 hour. Use Table 1.

Find the probability that talk time/battery life between charges for a randomly selected cell phone is below 3.3 hours. (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

Find the probability that talk time/battery life between charges for a randomly selected cell phone is both more than 4 hours and below 2.1 hours. (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

Twenty one percent of the time, talk time between charges is below a particular value. What is this value? (Round "z" value to 2 decimal places and final answer to 3 decimal places.)

Average talk time between charges of a cell phone battery is advertised as 3.6 hours. Assume that talk time/battery life is normally distributed with a standard deviation of 0.8 hour. Use Table 1.

Explanation / Answer

Solution:

(a) P(X < 3.3) = P((X-mean)/s <(3.3-3.6)/0.8) = P(Z < -0.375) = 0.352 (from standard normal table)

(b) P(X< 2.1 or X > 4) = P(Z <(2.1-3.6)/0.8) + P(Z >(4 - 3.6)/0.8)
= P (Z < ?1.88) + P(Z > 0.5 )
= 0.0301+0.3085
= 0.3386

(c) P(X<c)=0.21

=> P(Z<(c-3.6)/0.8) =0.21

=> (c-3.6)/0.8 = -0.81 (from standard normal table)

=> c = 3.6-0.81*0.8
= 2.952

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