Several states, including California, have passed legislation requiring automakers to sell a certain percentage of zero-emissions cars within their borders. One current alternative is battery-powered cars. The major problem with battery-operated cars is the limited time they can be driven before the batteries must be recharged. Longlife Battery, a start-up company, has developed a battery pack it claims will power a car at a sustained speed of 45 miles per hour for an average of 8 hours. But of course there will be variations: Some battery packs will last longer and some shorter than 8 hours. Current data indicate that the standard deviation of battery operation time before a charge is needed is 0.4 hours. Data show a normal distribution of uptime on these battery packs. Automakers are concerned that batteries may run short. For example, drivers might find an “8-hour” battery that lasts 7.5 hours or less unacceptable.

Question

a) What are the chances of this happening with the Longlife battery pack?

b) The automakers will accept no more than a 2% chance. Longlife Battery asks the question, what would the mean uptime have to be to meet the 2% requirement?

Answer 1

http://davidmlane.com/hyperstat/z_table.html

Answer 2

a) 0.1056
b) 6.676