Answer:
47.5%
Step-by-step explanation:
Given that :
Mean request (m) = 58
Standard deviation (σ) = 10
Find the approximate percentage of lightbulb replacement requests numbering between 38 and 58
Using the empirical formula :
According to the empirical rule;
68% of data lies within 1 standard deviation (σ) of the mean (m) [(m-σ) and (m+σ)]
95% of data lies within 2 standard deviation of the mean [(m-2σ) and (m+2σ)]
97.5% lies within 3 standard deviation of the mean [(m-3σ) and (m+3σ)]
To obtain the percentage numbering between 38 and 58
Mean of 58 and score of 38 shows the data lies within 2 standard deviations from the mean
Score of 38 lies 2 standard deviations below the mean (m - 2σ)
58 - 2(10) = 58 - 20 = 38
Since 95% = [(m-2σ) and (m+2σ)]
And our data is only 2 standard deviations below the mean and the other half is equal to the mean :
For a normal distribution, distribution is symmetric:
Thus the proportion 95% / 2 should give the percentage lightbulb replacement numbering between 38 and 58
95% / 2= 47.5%