Test a longer-life bulb claim using CLT

For many years the Consumer Union has found that the mean lifetime of a 100-watt light bulb is 72 days of continuous use, with standard deviation 12 days. The company markets a “new and improved” bulb yielding longer life. A sample of 55 new bulbs has average lifetime 75.2 days. Does this provide sufficient evidence of superiority at the 5% significance level?