Answer: 49.85%
Step-by-step explanation:
Given : The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped ( normal distribution ) and has a mean of 61 and a standard deviation of 9.
i.e. Â [tex]\mu=61[/tex] and [tex]\sigma=9[/tex]
To find : Â The approximate percentage of lightbulb replacement requests numbering between 34 and 61.
i.e. The approximate percentage of lightbulb replacement requests numbering between 34 and [tex]34+3(9)[/tex].
i.e. i.e. The approximate percentage of lightbulb replacement requests numbering between [tex]\mu[/tex] and [tex]\mu+3(\sigma)[/tex]. (1)
According to the 68-95-99.7 rule, about 99.7% of the population lies within 3 standard deviations from the mean.
i.e. about 49.85% of the population lies below 3 standard deviations from mean and 49.85% of the population lies above 3 standard deviations from mean.
i.e.,The approximate percentage of lightbulb replacement requests numbering between [tex]\mu[/tex] and [tex]\mu+3(\sigma)[/tex] = 49.85%
⇒ The approximate percentage of lightbulb replacement requests numbering between 34 and 61.= 49.85%
Answer:
According to 68-95-99.7 rule, 68%, 95% and 99.7% of data values lie within 1, 2 and 3 standard deviations of mean.
Here, mean = 57
Standard deviation = 11
The value 57 is the mean and hence, 50% of values are above mean
57 + 2 x 11 = 79
79 is 2 standard deviations above mean
Of the 95% that lies within 2 standard deviations of mean, half lies above mean and half lies below mean.
Therefore, approximate percentage of lightbulb replacement requests numbering between 57 and 79 = 95/2
= 47.5%
