Answer:
p = 0.635
Step-by-step explanation:
A step to the right is n and on ten different days, it was recorded to be
14, 13, 11, 12, 11, 12, 16, 16, 14, 8.
n = average of all the steps,
The average is the sum of variables divided by the number of variables
Average = (14+13+11+12+11+12+16+16+14+8)/10
Average = 12.7 steps.
σₙ² = variance of n
Variance is an average of the squared deviations from the mean.
[Σ(x - xbar)²/N]
Σ(x - xbar)² = (14-12.7)² + (13- 12.7² + (11-12.7)² + (12-12.7)² + (11-12.7)² + (12-12.7)² + (16-12.7)² + (16-12.7)² + (14-12.7)² + (8-12.7)² = 54.1
Variance = σₙ² = (54.1/10) = 5.41
standard deviation = σₙ = √(variance) = √5.41 = 2.326.
The proportion, p can be computed in two ways.
Mean = Np or standard deviation = √[Np(1-p)]
where N = total number of steps = 20
Mean = 12.7 = 20p
p = (12.7/20) = 0.635
Or
Standard deviation = 2.326 = √[20p(1-p)]
5.41 = 20p - 20p²
20p² - 20p + 5.41 = 0
Solving the quadratic equation,
p = 0.5 + 0.143i or p = 0.5 - 0.143i
not a unique or feasible solution, hence, the probability of a step to the right remains p = 0.635
Hope this Helps!!!
