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Chapter 5: Q. 5.61. (page 210)

Diabetes Prevalence. In a report titled Behavioral Risk factor Surveillance System Summary Prevalence Report, the Centers for Distance control and Prevention Discuss the prevalence of diabetes in the Unites states. The following table provides a diabetes prevalence frequency distribution for the 50 U.S state based on the question "Hhave you ever been told by a doctor that you have diabetes?"

For a randomly selected, let

A = event that the state has a diabetes prevalence percentage of at least 8%

B = event that the state has a diabetes prevalence percentage of less than 7%

C= event that the state has a diabetes prevalence percentage of at least 6% but less than 13%

D = event that the state has a diabetes prevalence percentage of less than 9%

Describe each of the following event in words and determine the number of outcomes (states) that constitute each event.

Part (a) (not C)

Part (b) (A & B)

Part (c) (C or D)

Part (d) (C & B)

Short Answer

Expert verified

Part (a) Number of outcomes =2

Part (b) Number of outcomes =10

Part (c) Number of outcomes =49

Part (d) Number of outcomes =6

Step by step solution

01

Part (a) Step 1. Given information.

The table below shows the diabetes prevalence frequency distribution for the 50 states of the United States, based on:

Diabetes (%)Frequency
5 - under 61
6 - under 7
5
7 - under 813
8 - under 910
9 - under 109
10 - under 118
11 - under 122
12 - under 131
13 - under 14
1

A = event that the state has a diabetes prevalence percentage of at least 8%

B = event that the state has a diabetes prevalence percentage of less than 7%

C= event that the state has a diabetes prevalence percentage of at least 6% but less than 13%

D = event that the state has a diabetes prevalence percentage of less than 9%

02

Part (a) Step 1.  In words, the event (not C) and the number of outcomes that make up the event.

(not C) is the event that includes all outcomes that aren't in C, therefore diabetes prevalence is either less than 6% or greater than 13%. Hence

Number of outcomes (not C)

1+1=2

03

Part (b) Step 1. Given information.

The table below shows the diabetes prevalence frequency distribution for the 50 states of the United States, based on:

Diabetes (%)Frequency
5 - under 61
6 - under 7
5
7 - under 813
8 - under 910
9 - under 109
10 - under 118
11 - under 122
12 - under 131
13 - under 14
1

A = event that the state has a diabetes prevalence percentage of at least 8%

B = event that the state has a diabetes prevalence percentage of less than 7%

C= event that the state has a diabetes prevalence percentage of at least 6% but less than 13%

D = event that the state has a diabetes prevalence percentage of less than 9%

04

Part (b) Step 2.  In words, the event (A & B) and the number of outcomes that make up the event

(A & B) is the event in which the state has a diabetes prevalence of at least 8% but less than 9%.

Number of outcomes

(A&B)=10

05

Part (c) Step 1. Given information.

The table below shows the diabetes prevalence frequency distribution for the 50 states of the United States, based on:

Diabetes (%)Frequency
5 - under 61
6 - under 7
5
7 - under 813
8 - under 910
9 - under 109
10 - under 118
11 - under 122
12 - under 131
13 - under 14
1

A = event that the state has a diabetes prevalence percentage of at least 8%

B = event that the state has a diabetes prevalence percentage of less than 7%

C= event that the state has a diabetes prevalence percentage of at least 6% but less than 13%

D = event that the state has a diabetes prevalence percentage of less than 9%

06

Part (c) Step 2.  In words, the event (C or D) and the number of outcomes that make up the event

When a state's diabetes prevalence is between 6 and 13 percent or less than 9 percent, it is classified as (C or D).

Number of outcomes

(CorD)=1+5+13+10+9+8+2+1=49

07

Part (d) Step 1. Given information.

The table below shows the diabetes prevalence frequency distribution for the 50 states of the United States, based on:

Diabetes (%)Frequency
5 - under 61
6 - under 7
5
7 - under 813
8 - under 910
9 - under 109
10 - under 118
11 - under 122
12 - under 131
13 - under 14
1

A = event that the state has a diabetes prevalence percentage of at least 8%

B = event that the state has a diabetes prevalence percentage of less than 7%

C= event that the state has a diabetes prevalence percentage of at least 6% but less than 13%

D = event that the state has a diabetes prevalence percentage of less than 9%

08

Part (d) Step 2.  In words, the event (C & B) and the number of outcomes that make up the event

(C & B) is the case where the state's diabetes prevalence is less than 7%.

Number of outcomes(C&D)1+5=6

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