Question

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 according to the line of best fit, about how many times would the coin land heads up in 100 flips? 48 50 51 53

Explanation:

Step1: Calculate the slope

Let \(x\) be the number of coin flips and \(y\) be the number of heads up.
Take two points \((10,7)\) and \((90,45)\)
Slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{45 - 7}{90 - 10}=\frac{38}{80}=0.475\)

Step2: Find the equation of the line

Using the point - slope form \(y - y_1=m(x - x_1)\), with \((x_1,y_1)=(10,7)\)
\(y - 7=0.475(x - 10)\)
\(y=0.475x - 4.75+7\)
\(y = 0.475x+2.25\)

Step3: Predict for \(x = 100\)

Substitute \(x = 100\) into \(y=0.475x + 2.25\)
\(y=0.475\times100+2.25\)
\(y=47.5+2.25=49.75\approx50\)

Answer:

50