Average talk time between charges of a cell phone battery is advertised as 4 hou

Question

Average talk time between charges of a cell phone battery is advertised as 4 hours. Assume that talk a. Find the probability that talk time/battery life between charges fora randomly selected cell phone is below 3 hours. (Round "z"value to 2 decimal places and final answer to 4 decimal places.) Probability b. Find the probability that talk time/battery life between charges for a randomly selected cell phone is both more than 5 hours and below 1.8 hours. (Round "z" value to 2 decimal places and final answer to 4 decimal places.) Probability c. Twenty five 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.)

Explanation / Answer

Solution:- Given that mean = 4 , sd = 1.4

a) P(X < 3) = P(Z < (X-mean)/s)
= P(Z < (3-4)/1.4)
= P(Z < -0.71)
= 1 P(Z < 0.71)
= 1 0.7611
= 0.2389

b. P(X < 1.8 or X > 5) = P(Z < (1.8-4)/1.4) + P(Z > (5-4)/1.4)
= P(Z < -1.57) + P(Z > 0.71)
= 0.0582 + 0.2389
= 0.2971

c. P(X<x)=0.25
(x-4)/1.4 = -0.67
x = 4 - (0.67*1.4)
x = 3.0620
  

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