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-Is this a valid probability distribution? Explain. -Display the probability dis

ID: 3200717 • Letter: #

Question

-Is this a valid probability distribution? Explain.

-Display the probability distribution in tabular form.

-What is the probability that a randomly selected male college student began shaving at age 16?

-What is the probability that a randomly selected male college student began shaving at least age 15?

-Calculate ? and ?, and interpret ?.

-Compute the interval ( ? – 2?, ? + 2? ).

-Find the probability that x falls within the interval of part g. Compare your results to the Empirical Rule.

p(x) 267 240 25 .213 20 15 093 10 067 067 05 .027 .013 .013 11 12 13 14 15 16 17 18 19 20 Shaving age (years)

Explanation / Answer

Answer:

a).

?p =1, and all p are 0 to 1. This is a valid probability distribution.

b).

x

p

11

0.013

12

0

13

0.027

14

0.067

15

0.213

16

0.267

17

0.24

18

0.093

19

0.067

20

0.013

Total

1

c).

P( x=16) = 0.267

d).P( x ?15) =0.893

e).

x

p(x)

x*p(x)

(x-mean)^2*p(x)

11

0.013

0.143

0.018286

12

0

0

0

13

0.027

0.351

0.01789

14

0.067

0.938

0.22047

15

0.213

3.195

1.686661

16

0.267

4.272

3.883941

17

0.24

4.08

5.561903

18

0.093

1.674

3.143641

19

0.067

1.273

3.11085

20

0.013

0.26

0.793762

1.000

16.186

18.4374

Mean=16.186

Variance =18.4374

Standard deviation = sqrt(18.4374)= 4.293879

-Compute the interval ( ? – 2?, ? + 2? ).

? – 2? =16.186-2*4.293879 =7.59824

? +2? =16.186+2*4.293879 =24.7738

within the interval (7.59824, 24.7738) all the observed data point falls ie 100% data falls in the interval.

This support the results to the Empirical Rule of ( ? – 2?, ? + 2? ) contains 95% of data.

x

p

11

0.013

12

0

13

0.027

14

0.067

15

0.213

16

0.267

17

0.24

18

0.093

19

0.067

20

0.013

Total

1