Question

A study of tattoos found the following:

Tattoo (T) No Tattoo (T')

Millennial(M) 200 800 1000

Not Millennial (M') 300 400 700

500 1200 1700

Compute these probabilities:

(1) P (Millennial and Tattoo)

(2) P (Millennial)

(3 P (Mlilennial / Tattoo)

(4) P (Millennial or Tattoo)

(5) P (Tatoo / Millenial)

(6) Is there a relationship between being a millennial and having a tattoo?

Problem B:

Suppose basketball players have an average life, normally distributed, of 80 years with a population standard deviation of 9 years.

7)What percent of basketball players will live more than 96 years?

8) What percent of basketball players will not make it past the age of 60?

9) Calculate the 96th percentile.

10) Calculate the 2nd percentile.

11) What proportion of basketball players will live between 70 and 85 years.

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Can you answer questions #’s 1-11? Can you show the calculations for each problem?

Answer 1

                                 Tattoo (T)                No Tattoo (T')               Total

Millennail                        200                        800                         1000

No Millennail                  300                          400                         700

Total                              500                         1200                       1700

(1) P(Millennail AND Tatto) = 200/1700 = 0.1176

(2) P(Millennai) = 1000/1700 = 0.5882

(3) P(Millennai/ Tattoo) = P(Millennai AND Tattoo)/P(Tattoo) = 200/500 = 0.4

(4) P(Millennai OR Tattoo) = P(Millennai) + P(Tattoo) - P(Millennai AND Tattoo)

                                      = 1000/1700 + 500/1700   - 200/1700

                                       = 0.5882 + 0.2941 - 0.1176 = 0.7647

(5) P(Tattoo/ Millennai) = P(Tattoo AND Millennai)/P(Millennai) = 200/1000 = 0.2

(6) We have :
P(Millennai) = 1000/1700 = 0.5882

P(Tattoo) = 500/1700 = 0.2941

So,

P(Millennai) X P(Tattoo) = 0.5882 X 0.2941 = 0.1730

P(Millennai AND Tattoo) = 200/1700 = 0.1176

Since P(Millennai) X P(Tattoo) P(Millennai AND Tattoo), there is a relationship between being a millennial and having a tattoo.

(7)

= 80

= 9

Z = (96 - 80)/9 = 1.7778

Table of Area Under Standard Curve gives area = 0.4625

So,

P(X>96) = 0.5 - 0.4625 = 0.0375 = 3.75 %

(8)

Z = (60 - 80)/9 = - 2.2222

Table gives area = 0.4868

So,

P(X<60 ) = 0.5 + 0.4868 = 0.9868

(9) 96th perntile corresponds to area = 0.96 - 0.5 = 0.46 from mid value to Z on RHS.

Table gives Z = 1.75

So,

Z = 1.75 = (X - 80)/9

So,

X = 80 + (1.75 X 9) = 95.75

(10)

3nd percentile corresponds to area = 0.5 - 0.02 = 0.48 from mid value to Z on LHS.

Table gives Z = - 2.08

So,

Z = - 2.08 = (X - 80)/9

So,

X = 80 - (2.08 X 9) = 61.28

(11)
Case 1:from X = 70 to mid value:

Z = (70 - 80)/9 = - 1.1111

Table gives area = 0.3665

Case 2: X from mid value to 85:
Z = (85 - 80)/9 = 0.5555

Table gives area = 0.2088

So,

P(70 < X < 85) = 0.3665 + 0.2088 = 0.5753