-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
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.