To determine the number of times the coin would land heads up in 100 flips based on the line of best fit, we'll go through a step-by-step process. This involves using the linear regression equation derived from the given data points.
1. Formulate the Problem:
We are given a table of data points, representing the number of coin flips and the corresponding number of heads observed. We need to establish a linear relationship between these two variables using the line of best fit. The general equation of a line is:
[tex]\[ y = mx + b \][/tex]
where [tex]\( y \)[/tex] is the number of heads, [tex]\( x \)[/tex] is the number of flips, [tex]\( m \)[/tex] is the slope, and [tex]\( b \)[/tex] is the y-intercept.
2. Identify the Slope (m) and Intercept (b):
After applying linear regression to the data points:
- The slope [tex]\( m \)[/tex] is approximately [tex]\( 0.5079 \)[/tex]
- The y-intercept [tex]\( b \)[/tex] is approximately [tex]\( 2.1455 \)[/tex]
3. Use the Line of Best Fit to Predict Number of Heads for 100 Flips:
Substitute [tex]\( x = 100 \)[/tex] into the equation of the line:
[tex]\[ y = mx + b \][/tex]
4. Calculate the Expected Number of Heads:
[tex]\[
y = 0.5079 \cdot 100 + 2.1455
\][/tex]
[tex]\[
y \approx 50.79 + 2.1455
\][/tex]
[tex]\[
y \approx 52.93
\][/tex]
5. Round to the Nearest Whole Number:
The calculated value of 52.93, rounded to the nearest whole number, is 53.
Therefore, according to the line of best fit, the coin would land heads up approximately 53 times in 100 flips.
Answer: 53
