The Fiat 500E is an electric car that can travel approximately 80–100 miles on a full charge.26 The time it takes to fully recharge depends on the percent depleted, but is approximately normal with mean 2.2 hours and standard deviation 0.6 hour (on a 240-volt line). Suppose a random Fiat 500E is recharged.
a. What is the probability that the amount of time to fully recharge is between 1 and 2 hours?
b. What is the probability that the amount of time to fully recharge is more than 3 hours?
c. If the amount of time to fully recharge is less than 30 minutes, the car could still travel another 50 miles. What is the probability that the car could travel another 50 miles?
d. Suppose three Fiat 500E’s are selected at random. What is the probability that all three will have a time to fully recharge greater than 2.5 hours?
Oriental rugs are made from various wools and woven in several different countries. The pile height (in millimeters) of an Oriental rug varies slightly and can be modeled by a uniform random variable on the interval [6, 10].
a. Carefully sketch a graph of the density function for pile height.
b. What is the probability that a randomly selected Oriental rug will have pile height less than 7 mm?
c. What is the probability that a randomly selected Oriental rug will have pile height between 8.5 and 9.5 mm?
d. Find a value h such that 90% of all Oriental rugs have pile height less than h.