Stat - normal distribution

Question

The time until recharge for a battery in a laptop computer under common conditions is normally distributed with mean 260 minutes and standard deviation 50 minutes.

a) What is the probability that a battery lasts more than four hours? (Round the answer to 3 decimal places.)

b) What are the quartiles (the 25% and 75% values) of battery life? (Round the answer to the nearest integer.)

c) What value of life in minutes is exceeded with 95% probability? (Round the answer to the nearest integer.)

Answer 1

a) For this problem you need to calculate a Z score and use the normal probability Z table or technology to get the probability.

Z = (x - mean)/standard deviation

x is time of 4 hours in minutes, which is 240

Z = (240 - 260)/50

Z = -0.4

P(Z > -0.4) = P(Z < 0.4) = 0.6554

b) To find the quartiles,

Find Z values for the lower 25% and the upper 25% of the data, which is -0.67 and 0.67

Mean + Z*standard deviation

250 + (-0.67)(50) = 216.50 (25%)

250 + (0.67)(50) = 283.50 (75%)

c) To find what value is exceeded with 95% probability, find the Z value for bottom 5%, so look up .0500 on the Z table, which is -1.65

mean + Z*standard deviation

250 + (-1.65)(50) = 167.50