Answer:
47.5% of these led lights have lifetime between 7.9 and 8.9 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 = 7.9 hours
Standard deviation = 0.5 hours
The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.
Lifetime between 7.9 and 8.9 hours:
7.9 hours is the mean.
8.9 = 7.9 + 2*0.5
So 8.9 hours is two standard deviations above the mean.
Of the 50% of the measures that are above the mean, 95% are between the mean of 7.9 and two standard deviations above the mean(8.9). So
0.5*0.95 = 0.475
47.5% of these led lights have lifetime between 7.9 and 8.9 hours.
