Answer:
34% of lightbulb replacement requests numbering between 47 and 52
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 = 52
Standard deviation = 5
Between 47 and 52:
52 is the mean and 47 is one standard deviation below the mean.
By the Empirical Rule, 68% of the measures are within 1 standard deviation of the mean.
Since the normal distribution is symmetric, of those, 34% are within 1 standard deviation below the mean and the mean(47 and 52) and 34% are within the mean and one standard deviation above the mean(52 and 57).
So
34% of lightbulb replacement requests numbering between 47 and 52
