Respuesta :
Answer:
the approximate percentage of light bulb replacement requests between 63 and 75 is 47.5%
Step-by-step explanation:
the 68-95-99.7 rule for a bell-shaped distribution states that
68% of the population is found between mean+ 1 standard deviation and the mean - 1 standard deviation
95% of the population is found between mean+ 2 standard deviations and the mean - 2 standard deviations
99.7% of the population is found between mean+ 3 standard deviations and the mean - 3 standard deviations
therefore since the
light bulbs = mean + x * standard deviation
75 = 63 + x* 6
x= (75-63)/6 = 2
therefore
mean + 2 * standard deviation = 75
mean - 2 standard deviations = 63- 2*6 = 51
and
95% of the light bulbs replacement requests are found between 51 and 75 daily requests
since the bell shaped distribution is symmetrical
95%/2 = 47.5 % is found between mean and mean + 2 * standard deviation
thus
47.5 % of the light bulbs replacements are found between 63 and mean + 2 * standard deviation = 75
47.5 % of the light bulbs replacements are found 51 and 63
Using the Empirical Rule, the approximate percentage of light bulb replacement requests numbering between 63 and 75 is of 47.5%.
According to the Empirical Rule, in a normal distribution:
- 68% of the measures are within 1 standard deviation of the mean.
- 95% are within 2.
- 99.7% are within 3.
- The normal distribution is symmetric, which means that 50% of the measures are above the mean and 50% are below.
In this problem:
- Mean of 63, standard deviation of 6.
- 75 = 63 + 2(6), which means that 75 is two standard deviations above the mean.
- Of the 50% of the measures below the mean, 95% are between 63 and 75, so:
[tex]0.95(50) = 47.5[/tex]
The approximate percentage of light bulb replacement requests numbering between 63 and 75 is of 47.5%.
A similar problem is given at https://brainly.com/question/24244232
