In your bid to be elected class representative, you have your election committee survey five randomly chosen students in your class and ask them to rank you on a scale of 0-10. Your rankings are 9, 6, 1, 7, 7. (a) Find the sample mean and standard deviation. (Round your answers to two decimal places.) HINT [See Example 1.] sample mean standard deviation (b) Assuming the sample mean and standard deviation are indicative of the class as a whole, in what range does the empirical rule predict that approximately 68% of the class will rank you

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Respuesta :

mahamnasir mahamnasir · Answer 1 · 2020-08-14T15:02:33+02:00

Answer:

Sample mean = 6

Sample standard deviation = 3

Range = 3 to 9

Step-by-step explanation:

Given data:

Rankings (x)

9

6

1

7

sample size = n = 5

(a)

Sample Mean: [tex]\frac{}{x}[/tex] = ∑x/n

= 9+6+1+7+7 / 5

= 30 / 5

[tex]\frac{}{x}[/tex] = 6

Sample Standard Deviation = s = √(x- [tex]\frac{}{x}[/tex] )²/n-1

= √((9-6)² + (6-6)² + (1-6)² + (7-6)² + (7-6)²) / (5-1)

= √((3)² + (0)² + (-5)² + (1)² + (1)²) / 4

= √(9+0+25+1+1)/4

= √36 / 4

= √9

= 3

s = 3

b) In what range does the empirical rule predict that approximately 68% of the class will rank you?

As per the empirical rule, 68% of data falls within first standard deviation from the mean μ ± 1σ

[tex]\frac{}{x}[/tex] = 6

s = 3

So

6 - 3 = 3

6 + 3 = 9

Hence the range is from 3 to 9