6. The lifetime of lightbulbs that are advertised to last for 4100 hours are normally distributed with a mean of 4400 hours and a standard deviation of 300 hours. What is the probability that a bulb lasts longer than the advertised figure? 7. A new car that is a gas- and electric-powered hybrid has recently hit the market. The distance travelled on 1 gallon of fuel is normally distributed with a mean of 65 miles and a standard deviation of 7 miles. Find the probability of the following events: a. The car travels more than 69 miles per gallon. Probability = b. The car travels less than 58 miles per gallon. Probability = c. The car travels between 61 and 71 miles per gallon. Probability = 8. Select True or False 1. A random variable X is normally distributed with a mean of 150 and a variance of 36. Given that X = 120, its corresponding z- score is 5.0 2. Let z1 be a z-score that is unknown but identifiable by position and area. If the symmetrical area between -z1 and +z1 is 0.9544, the value of z1 is 2.0 3. The mean and standard deviation of a normally distributed random variable which has been standardized are one and zero, respectively._ 4. Using the standard normal curve, the z-score representing the 90th percentile is 1.28. 9. Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this is not always possible. An analysis of the amount of interest paid monthly by a bank's Visa cardholders reveals that the amount is normally distributed with a mean of 27 dollars and a standard deviation of 8 dollars. a. What proportion of the bank's Visa cardholders pay more than 31 dollars in interest? Proportion = b. What proportion of the bank's Visa cardholders pay more than 36 dollars in interest? Proportion = C. What proportion of the bank's Visa cardholders pay less than 16 dollars in interest? Proportion =_ d. What interest payment is exceeded by only 21% of the bank's Visa cardholders? Interest Payment =_ 10. The following density function describes a random variable X. 1 ( x ) - 1 - ( x /2) if 0