A Gold Canyon candle is designed to last nine hours. However, depending on the wind, air bubbles in the wax, the quality of the wax, and the number of times the candle is re-lit, the actual burning time (in hours) is a uniform random variable with a =6.5 and b = 10.5. Suppose one of these candles is randomly selected.
a. Find the probability that the candle burns at least seven hours.
b. Find the probability that the candle burns at most eight hours.
c. Find the mean burning time and the probability that the burning time of a randomly selected candle will be within one standard deviation of the mean.
d. Find a time t such that 25% of all candles burn longer than t hours.
According to Major League Baseball rules, a baseball should weigh between 5 and 5.25 ounces and have a circumference of between 9 and 9.25 inches. Suppose the weight of a baseball (in ounces) has a uniform distribution with a 5 5.085 and b 5 5.155, and the circumference (in inches) has a uniform distribution with a = 9.0 and b = 9.1.
a. Find the probability that a randomly selected baseball has a weight greater than 5.14 ounces. Write a Solution Trail for this problem.
b. Find the probability that a randomly selected baseball has a circumference less than 9.03 inches.
c. Suppose the weight and the circumference are independent. Find the probability that a randomly selected baseball will have a weight between 5.11 and 5.13 ounces and a circumference between 9.04 and 9.06 inches.