Question

Studies show that most children need an average of ten hours per sleep, while most adults only require an average of seven hours of sleep. The data shown on the scatter plot below represents the relationship between a young boy’s age (in months) and the average number of hours that he sleeps each night.
Part A: Use the equation of the best fit line Y = -1/8x + 113/8, to mathematically predict how much sleep the boy will average each night when he is 5 years old. Use complete sentences to explain why or why not this is a resonable prediction.

Part B: Use the equation of the best fit line Y = -1/8x + 113/8, to mathematically predict how much sleep the boy will average each night when he is 20 years old. Use complete sentences to explain why or why not this is a reasonable prediction?

Answer 1

Solution:

Part A

The line of best fit for a five year children is given as

$Y =\frac {-x}{8} +\frac{113}{8},$

When children is 5 , years old, average that children will sleep each night

can be calculated by , putting, x=5 in above equation

$Y=\frac {-5}{8} +\frac{113}{8}\\\\ Y=\frac{108}{8}\\\\ Y=13.5$

Average sleep of 5 year old children , given by line of best fit= 13.5 hours

But it is given that, Average that a five year old children sleep= 10 hours

Difference between calculated and Actual = 13.5 - 10 = 3.5 hours, which is not so large,for a five year old children, but a large value, showing that it is not a reasonable estimate.

Part B

The line of best fit for a 20 year old  is given as

$Y =\frac {-x}{8} +\frac{113}{8},$

When adult who  is 20 , years old, average that adult will sleep each night

can be calculated by , putting, x=20 in above equation

$Y=\frac {-20}{8} +\frac{113}{8}\\\\ Y=\frac{93}{8}\\\\ Y=11.625$

Average sleep of 20 year old adult , given by line of best fit= 11.625 hours

But it is given that, Average that a 20 year old adult sleeps= 7 hours

Difference between calculated and Actual = 11.625 - 7 = 4.625 hours, which is quite large, for an adult, showing that it is not a reasonable estimate.