Question

1. The time until recharge for a battery in a laptop computer under common conditions is normally distributed with a mean of 260 minutes and a standard deviation of 50 minutes.
   1. What is the probability that a battery lasts more than four hours?
   2. What are the quartiles (25% and 75%) of battery life?
   3. What value of battery life, in minutes, is exceeded with 95% probability?

Answer 1

Here it is given that distribution is normal with mean of 260 minutes and a standard deviation of 50 minutes.

a.

As distribution is normal we can convert x to z

b. For 25% z value is

Using z value table we get z=-0.674

So

So

Similarly for 75%,

Using z table we get z=0.674

So

c. Now we need to find x such that

Using z table we get z=-1.645

Using formula of z we get