To determine how many times the coin would land heads up in 100 flips, we can use the line of best fit obtained from the experiment data. The line of best fit is found using a linear model, which provides us with the equation of a straight line in the form:
[tex]\[ \text{Number of Heads} = (\text{slope} \times \text{Number of Flips}) + \text{intercept} \][/tex]
From the analysis of the data provided, the slope and intercept of the line of best fit are given by:
[tex]\[ \text{slope} = 0.49818182 \][/tex]
[tex]\[ \text{intercept} = 0.98181818 \][/tex]
Using these values, we can predict the number of heads for any given number of flips. Specifically, for 100 flips, the prediction is calculated as follows:
[tex]\[ \text{Number of Heads for 100 flips} = (0.49818182 \times 100) + 0.98181818 \][/tex]
Performing the multiplication and addition, we get:
[tex]\[ \text{Number of Heads for 100 flips} = 49.818182 + 0.98181818 \][/tex]
[tex]\[ \text{Number of Heads for 100 flips} = 50.800000000000004 \][/tex]
Therefore, according to the line of best fit, the number of times the coin would land heads up in 100 flips is approximately 50.8. When considering the closest whole number options provided (48, 50, 51, 53), we round 50.8 to the nearest whole number, which is 51.
So, the expected number of heads in 100 flips is approximately 51.
