lydia runs an experiment to determine if a coin is fair by counting the number of times a coin lands heads…

lydia runs an experiment to determine if a coin is fair by counting the number of times a coin lands heads up. the table shows her data. coin fairness test number of coin flips 0 10 20 30 40 50 60 70 80 90 number of heads up 0 7 12 18 23 30 35 38 42 45 according to the line of best fit, about how many times would the coin land heads up in 100 flips? 48 50 51 53

lydia runs an experiment to determine if a coin is fair by counting the number of times a coin lands heads up. the table shows her data. coin fairness test number of coin flips 0 10 20 30 40 50 60 70 80 90 number of heads up 0 7 12 18 23 30 35 38 42 45 according to the line of best fit, about how many times would the coin land heads up in 100 flips? 48 50 51 53

Answer

Explanation:

Step1: Assume a linear relationship

Let the number of coin - flips be $x$ and the number of heads - up be $y$. We can use the two - point form of a line $y - y_1=\frac{y_2 - y_1}{x_2 - x_1}(x - x_1)$. Let's take two points from the data, say $(10,7)$ and $(90,45)$.

Step2: Calculate the slope

The slope $m=\frac{45 - 7}{90 - 10}=\frac{38}{80}=0.475$.

Step3: Use the point - slope form with the point $(10,7)$

The equation of the line is $y - 7=0.475(x - 10)$.

Step4: Expand the equation

$y-7 = 0.475x-4.75$, so $y=0.475x + 2.25$.

Step5: Substitute $x = 100$

When $x = 100$, $y=0.475\times100+2.25=47.5 + 2.25=49.75\approx50$.

Answer:

50