PRACTICE OF STATISTICS F/AP EXAM
PRACTICE OF STATISTICS F/AP EXAM
6th Edition
ISBN: 9781319113339
Author: Starnes
Publisher: MAC HIGHER
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Chapter 9.1, Problem 33E

(a)

To determine

To find: the numbers of the mathematics degrees given that year were earned by women.

(a)

Expert Solution
Check Mark

Answer to Problem 33E

10258 women

Explanation of Solution

Given:

  P(Bachelor)=70%=0.70P(Master)=24%=0.24P(women/Bachelor)=43%=0.43P(women/Master)=41%=0.41P(women/doctorate)=29%=0.29

Formula used:

General multiplication rule:

  P(A and B)=P(AB)=P(A)×P(B/A)=P(B)×P(A/B)

Addition rule

  P(AB)=P(A or B)=P(A)+P(B)

Calculation:

70% of the mathematics degrees were Bachelor degrees, whereas 24% were master degrees and in total there need to have been 100% degrees. This then implies that 100%-70%-24%=6% of the mathematics degrees were doctorates.

  P(Doctorates)=67%=0.06

Using the general multiplication rule:

  P(women and Bachelor)=P(Bachelor)×P(women/Bachelor)=0.70×0.43=0.301P(women and Master)=P(Master)×P(women/Master)=0.24×0.41=0.0984P(women and doctorate)=P(Doctorates)×P(women/doctorate)=0.06×0.29=0.0174

Using the addition rule

  P(women)=P(women/Bachelor)+P(women/Master)+(women/doctorate)=0.301+0.0984+0.0174=0.4168

Thus a proportion of 0.4168 of the 24611 degrees were earned by the women.

Which are associates with =0.4168×24611=10257.864=10258 women

(b)

To determine

To Explain: that the events are independent yes or no.

(b)

Expert Solution
Check Mark

Answer to Problem 33E

Not independent

Explanation of Solution

Given:

  P(Bachelor)=70%=0.70P(Master)=24%=0.24P(women/Bachelor)=43%=0.43P(women/Master)=41%=0.41P(women/doctorate)=29%=0.29

Formula used:

Multiplication rule:

  P(A and B)=P(AB)=P(A)×P(B/A)=P(B)×P(A/B)

Addition rule

  P(AB)=P(A or B)=P(A)+P(B)

Calculation:

70% of the mathematics degrees were Bachelor degrees, whereas 24% were master degrees and in total there need to possess been 100% degrees. This then implies that 100%-70%-24%=6% of the mathematics degrees were doctorates.

  P(Doctorates)=67%=0.06

Multiplication rule:

  P(women and Bachelor)=P(Bachelor)×P(women/Bachelor)=0.70×0.43=0.301P(women and Master)=P(Master)×P(women/Master)=0.24×0.41=0.0984P(women and doctorate)=P(Doctorates)×P(women/doctorate)=0.06×0.29=0.0174

Using the addition rule

  P(women)=P(women/Bachelor)+P(women/Master)+(women/doctorate)=0.301+0.0984+0.0174=0.4168

It is find that the possibilities P(women)=0.4168 and P(women/Bachelor)=0.43 are not equal, which suggests that the likelihood of the event “Degree earned by a woman” is have an effect on once grasp that the degree was a Bachelor’s degree.

(c)

To determine

To find: the probability that at least 1 of the 2 degrees was earned by a women.

(c)

Expert Solution
Check Mark

Answer to Problem 33E

0.65987776=65.987776%

Explanation of Solution

Given:

  P(Bachelor)=70%=0.70P(Master)=24%=0.24P(women/Bachelor)=43%=0.43P(women/Master)=41%=0.41P(women/doctorate)=29%=0.29

Formula used:

Multiplication rule:

  P(A and B)=P(AB)=P(A)×P(B/A)=P(B)×P(A/B)

Addition rule

  P(AB)=P(A or B)=P(A)+P(B)

Complement rule:

  P(A)=P(not A)=1P(A)

Multiplication rule for independent events:

  P(AB)=P(A and B)=P(A)×P(B)

Calculation:

70% of the mathematics degrees were Bachelor degrees, whereas 24% were master degrees and in total there require to have been 100% degrees. This then implies that 100%-70%-24%=6% of the mathematics degrees were doctorates.

  P(Doctorates)=67%=0.06

Use the general multiplication rule:

  P(women and Bachelor)=P(Bachelor)×P(women/Bachelor)=0.70×0.43=0.301P(women and Master)=P(Master)×P(women/Master)=0.24×0.41=0.0984P(women and doctorate)=P(Doctorates)×P(women/doctorate)=0.06×0.29=0.0174

Use the addition rule for disjoint events:

  P(women)=P(women/Bachelor)+P(women/Master)+(women/doctorate)=0.301+0.0984+0.0174=0.4168

Use the complement rule:

  P(Not woman)=1P(woman)=10.4168=0.5832

Use the multiplication rule for independent events (assuming that the two individuals are independent):

  P(Two Not woman)=P(Not woman)×P(Not woman)=0.5832×0.5832=0.34012224

Use the complement rule:

  P(At least one women)=1P(Two not woman)=10.3412224=0.65987776=65.987776%

Chapter 9 Solutions

PRACTICE OF STATISTICS F/AP EXAM

Ch. 9.1 - Prob. 11ECh. 9.1 - Prob. 12ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - Prob. 16ECh. 9.1 - Prob. 17ECh. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - Prob. 20ECh. 9.1 - Prob. 21ECh. 9.1 - Prob. 22ECh. 9.1 - Prob. 23ECh. 9.1 - Prob. 24ECh. 9.1 - Prob. 25ECh. 9.1 - Prob. 26ECh. 9.1 - Prob. 27ECh. 9.1 - Prob. 28ECh. 9.1 - Prob. 29ECh. 9.1 - Prob. 30ECh. 9.1 - Prob. 31ECh. 9.1 - Prob. 32ECh. 9.1 - Prob. 33ECh. 9.1 - Prob. 34ECh. 9.2 - Prob. 35ECh. 9.2 - Prob. 36ECh. 9.2 - Prob. 37ECh. 9.2 - Prob. 38ECh. 9.2 - Prob. 39ECh. 9.2 - Prob. 40ECh. 9.2 - Prob. 41ECh. 9.2 - Prob. 42ECh. 9.2 - Prob. 43ECh. 9.2 - Prob. 44ECh. 9.2 - Prob. 45ECh. 9.2 - Prob. 46ECh. 9.2 - Prob. 47ECh. 9.2 - Prob. 48ECh. 9.2 - Prob. 49ECh. 9.2 - Prob. 50ECh. 9.2 - Prob. 51ECh. 9.2 - Prob. 52ECh. 9.2 - Prob. 53ECh. 9.2 - Prob. 54ECh. 9.2 - Prob. 55ECh. 9.2 - Prob. 56ECh. 9.2 - Prob. 57ECh. 9.2 - Prob. 58ECh. 9.2 - Prob. 59ECh. 9.2 - Prob. 60ECh. 9.2 - Prob. 61ECh. 9.2 - Prob. 62ECh. 9.2 - Prob. 63ECh. 9.2 - Prob. 64ECh. 9.3 - Prob. 65ECh. 9.3 - Prob. 66ECh. 9.3 - Prob. 67ECh. 9.3 - Prob. 68ECh. 9.3 - Prob. 69ECh. 9.3 - Prob. 70ECh. 9.3 - Prob. 71ECh. 9.3 - Prob. 72ECh. 9.3 - Prob. 73ECh. 9.3 - Prob. 74ECh. 9.3 - Prob. 75ECh. 9.3 - Prob. 76ECh. 9.3 - Prob. 77ECh. 9.3 - Prob. 78ECh. 9.3 - Prob. 79ECh. 9.3 - Prob. 80ECh. 9.3 - Prob. 81ECh. 9.3 - Prob. 82ECh. 9.3 - Prob. 83ECh. 9.3 - Prob. 84ECh. 9.3 - Prob. 85ECh. 9.3 - Prob. 86ECh. 9.3 - Prob. 87ECh. 9.3 - Prob. 88ECh. 9.3 - Prob. 89ECh. 9.3 - Prob. 90ECh. 9.3 - Prob. 91ECh. 9.3 - Prob. 92ECh. 9.3 - Prob. 93ECh. 9.3 - Prob. 94ECh. 9.3 - Prob. 95ECh. 9.3 - Prob. 96ECh. 9.3 - Prob. 97ECh. 9.3 - Prob. 98ECh. 9.3 - Prob. 99ECh. 9.3 - Prob. 100ECh. 9.3 - Prob. 101ECh. 9.3 - Prob. 102ECh. 9.3 - Prob. 103ECh. 9.3 - Prob. 104ECh. 9.3 - Prob. 105ECh. 9.3 - Prob. 106ECh. 9.3 - Prob. 107ECh. 9.3 - Prob. 108ECh. 9.3 - Prob. 109ECh. 9.3 - Prob. 110ECh. 9 - Prob. R9.1RECh. 9 - Prob. R9.2RECh. 9 - Prob. R9.3RECh. 9 - Prob. R9.4RECh. 9 - Prob. R9.5RECh. 9 - Prob. R9.6RECh. 9 - Prob. R9.7RECh. 9 - Prob. T9.1SPTCh. 9 - Prob. T9.2SPTCh. 9 - Prob. T9.3SPTCh. 9 - Prob. T9.4SPTCh. 9 - Prob. T9.5SPTCh. 9 - Prob. T9.6SPTCh. 9 - Prob. T9.7SPTCh. 9 - Prob. T9.8SPTCh. 9 - Prob. T9.9SPTCh. 9 - Prob. T9.10SPTCh. 9 - Prob. T9.11SPTCh. 9 - Prob. T9.12SPTCh. 9 - Prob. T9.13SPT
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