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.

A 2-row table with 10 columns. The first row is labeled number of coin flips with entries 0, 10, 20, 30 ,40, 50, 60, 70, 80, 90. The second row is labeled number of heads up with entries 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 1

Fit a least-squares line to the data. Using the points (x = flips, y = heads) gives

slope ≈ 4190/8250 ≈ 0.5076 and intercept ≈ 25 − 0.5076(45) ≈ 2.159.

For 100 flips: y ≈ 2.159 + 0.5076(100) ≈ 52.92 ≈ 53.

Answer: 53.