An automobile battery manufacturer offers a 39/50 warranty on its batteries. The first number in the warranty code is the free-replacement period; the second number is the prorated-credit period. Under this warranty, if a battery fails within 39 months of purchase, the manufacturer replaces the battery at no charge to the consumer. If the battery fails after 39 months but within 50 months, the manufacturer provides a prorated credit toward the puchase of a new battery.
The maufacturer assumes that x, the lifetime of its auto batteries, is normally distrubuted with a mean of 44 months and a standard deviation of 3.6 months.
If the maufacturer's assumptions are correct, it would need to replace_____ of its batteries free of charge.
A. 8.23%
B. 4.75%
C. 91.77%
D. 95.25%