3. The number of broken bobble heads found on a bobble head production line every week follows a normal distribution with a mean of 10 bobble heads and a standard deviation of 2. Use the emperical rule and/or symmetry to justify your answers. A. What number of bobble heads broken in a given week would be considered the 84th percentile? Use the empircal rule and/or symmetry to justify answers. B. Would youu be surprised if, in a given week, less than 10 bobble heads were broken? Justify your answer. Use the empirical rule/and or symmetry to justify answers. C. What range of weekly broken bobble heads would occur 95% of the time. Use the empirical rule and/or symmetry to justify answers.

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Asked Nov 17, 2019
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3. The number of broken bobble heads found on a bobble head production line every week follows a normal distribution with a mean of 10 bobble heads and a standard deviation of 2. Use the emperical rule and/or symmetry to justify your answers. 

A. What number of bobble heads broken in a given week would be considered the 84th percentile? Use the empircal rule and/or symmetry to justify answers. 

B. Would youu be surprised if, in a given week, less than 10 bobble heads were broken? Justify your answer. Use the empirical rule/and or symmetry to justify answers. 

C. What range of weekly broken bobble heads would occur 95% of the time. Use the empirical rule and/or symmetry to justify answers. 

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Expert Answer

Step 1

From the provided information, the mean (µ) and standard deviation (σ) are 10 and 2 respectively.

A.   Let the number of bobble heads broken in a given week is x. The z score at 84th percentile from the z score table is 1.

Now, the required number of bobble can be obtained as;

x -
r-10
2
2 x10
x 2+10
r 12
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x - r-10 2 2 x10 x 2+10 r 12

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Step 2

Using the empirical rule, 99.7% of the data lie within three standard deviation from the mean which can be obtained as;

30 10+3 x2
= 10 +6
=(4,16)
The value 12 lie in the interval. Thus, the number of bobble head broken in a given
week is 12
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Image Transcriptionclose

30 10+3 x2 = 10 +6 =(4,16) The value 12 lie in the interval. Thus, the number of bobble head broken in a given week is 12

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Step 3

B.  It would not be surprised if, in a given week less than 10 bobble heads were broken because the interval which contain...

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