A new extended-life light bulb has an average life of 750 hours, with a standard deviation of 50 hours. If the life of these light bulbs approximates a normal distribution, about what percent of the distribution will be between 600 hours and 900 hours?

99.7% of the distribution will be between 600 hours and 900 hours.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 750

Standard deviation = 50

What percent of the distribution will be between 600 hours and 900 hours?

600 = 750 - 3*50

600 is 3 standard deviations below the mean

900 = 750 + 3*50

900 is 3 standard deviations above the mean

By the Empirical Rule, 99.7% of the distribution will be between 600 hours and 900 hours.