Answer :
Answer:
2 to 11 ounces would be the interval.
Step-by-step explanation:
Add 3 standard deviations above and below the mean to get the range in which 99.7% of the data in a normal distribution will fall
6.5 + 4.5 = 11
6.5 - 4.5 = 2.
Hope this helped!
The interval that would represent the weights of the middle [tex]99.7\%[/tex] of all oranges from this orchard is between [tex]2.5[/tex] and [tex]11.5[/tex] such that weight and standard deviation are [tex]7\;\text{oz.}[/tex] and [tex]1.5\;\text{oz.}[/tex] respectively.
Empirical Rule
The empirical rule formula states that [tex]68\%,95\%[/tex] and [tex]99.7\%[/tex] of all the data can be represented in the interval of [tex]1, 2[/tex] and [tex]3[/tex] standard deviation of the mean respectively.
How to use the empirical rule formula to determine the interval?
Mean weight [tex]=7\;\text{oz.}[/tex]
Standard deviation [tex]=5\;\text{oz.}[/tex]
According to the empirical rule, [tex]99.7\%[/tex] of values lie within [tex]3[/tex] standard deviations of the mean.
So, we have to add and subtract [tex]1.5[/tex] three times in mean weight to obtain the required interval.
[tex]\Rightarrow7-4.5 < 7 < 7+4.5\\\Rightarrow2.5 < 7 < 11.5[/tex]
Thus, the interval that would represent the weights of the middle [tex]99.7\%[/tex] of all oranges from this orchard is between [tex]2.5[/tex] and [tex]11.5[/tex].
Learn more about empirical rule formula here- https://brainly.com/question/13815221
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