Question

Q1.
all students.
In a study on nutrition conducted in 1984, 18 normal adults aged 23 to 61 years old were measured for
body fat, which is given as percentage of weight. The mean (average) body fat percentage for women
40 years old was 28.6 percent, and for women 53 years old was 38.4 percent. Find a linear equation that
will tell you percentage of body fat based on a woman's age.
A.
B.
C.
What does your equation give for 20 years of age?
For 60?
Interpret the meaning of slope and y-intercept.​

Answer 1

Answer:

I think question is wrong

Answer 2

Given : The mean (average) body fat percentage for women

40 years old was 28.6 percent, and for women 53 years old was 38.4 percent.

To Find :  linear equation that will tell you percentage of body fat based on a woman's age.

Fat for 20 year of age

Fat for 60 year of age

Interpret the meaning of slope and y-intercept.​

Solution:

y  = Fat %

x =  age

slope = ( 38.4 - 28.6 ) / ( 53 - 40)

=  (9.8 ) / 13

= 98/130

= 49/65

y  - 28.6  = (49/65) (x  - 40)

=> 65y - 1859  = 49x  -  1960

=> 49x = 65y  + 101

49x = 65y  + 101  is the  linear equation that

will tell you percentage of body fat based on a woman's age.

x = 20

=>  49(20)  = 65y  + 101  => y  = 13.52 %

x = 60

=>  49(60)  = 65y  + 101  => y  = 43.68 %

49x = 65y  + 101

=> y  = 49x/65  - 101/65

Slope = 49/65

For each year of age fat increase by 49/65

 - 101/65 y intercept  shows that fat start building after some age , new born does not have fat

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