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In Exercises 5.16-5.26, express your probability answers as a decimal rounded to three places.

Cardiovascular Hospitalizations. From the Florida State Center for Health Statistics report Women and Cardiovascular Disease Hospitalization, we obtained the following table showing the number of female hospitalizations for cardiovascular disease, by age group, during one year.

One of these case records is selected at random. Find the probability that the woman was

(a) in her 50s.

(b) less than 50 years old.

(c) between 40 and 69 years old, inclusive.

(d) 70 years old or older.

Short Answer

Expert verified

Part (a) 0.100.

Part (b) 0.081

Part (c) 0.330

Part (d) 0.642

Step by step solution

01

Part (a) Step 1. Given information. 

The given statement is:

From the Florida State Center for Health Statistics report Women and Cardiovascular Disease Hospitalization, we obtained the following table showing the number of female hospitalizations for cardiovascular disease, by age group, during one year.

Age group(yrs)

Number

0-19

810

20-39

5,029

40-49

10,977

50-59

20,983

60-69

36,884

70-79

65,017

80 and over

69,167

02

Part (a) Step 2. Find the probability that the woman was in her 50s.

We know that an event's probability ranges from 0 to 1, and both 0 and 1 are included in it.

The formula for the probability of an event is:

P(E)=No.offavorableoutcomesTotalno.ofoutcomes

A total of 208,867 females were hospitalized for cardiovascular disease. Therefore, the total number of instances will become 208,867.

The total instances where the woman was in her 50s is:

20,983

Let's call the occurrence 'E' where a woman was in her 50s.

The probability that a woman was in her 50s is:

P(E)=20,9832,08,867=0.100

03

Part (b) Step 1. Find the probability that the woman was less than 50 years old.

The total instances where the woman was less than 50 years old are:

810+5,029+10,977=16,816

Let's call the occurrence 'E' where a woman was less than 50 years old.

The probability that the selected woman was less than 50 years old is:

P(E)=16,8162,08,867=0.081

04

Part (c) Step 1. Find the probability that the woman was between 40 and 69 years old, inclusive. 

The total instances where the woman was between 40 and 69 years old, inclusive:

10,977+20,983+36,884=68,844

Let's call the occurrence 'E' where a woman was between 40 and 69 years old, inclusive.

The probability that the selected woman was between 40 and 69 years old, inclusive is:

P(E)=68,8442,08,867=0.330

05

Part (d) Step 1. Find the probability that the woman was 70 years old or older.

The total instances where the woman was70 years old or older are:

65,017+69,167=1,34,184

Let's call the occurrence 'E' where a woman was 70 years old or older.

The probability that the selected woman was 70 years old or older is:

P(E)=1,34,1842,08,867=0.642

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