Answer:
A) μ = 91.2; σ = 9.3
B) No
Step-by-step explanation:
To find the mean, μ, we use the formula
μ = np, where n is the sample size and p is the probability of success (percentage of times the letter is used).
This gives us
μ = 0.057(1600) = 91.2
To find the standard deviation, we use the formula
σ = √(np(1-p)
This gives us
σ = √(1600×0.057×(1-0.057))
= √(1600×0.057×0.943) = √86.0016 = 9.2737 ≈ 9.3≈
Any value that is more than two standard deviations from the mean is considered unusual. The value 102 is
(102-91.2)/9.3 = 10.8/9.3 = 1.16 standard deviations from the mean. This is not statistically unusual.
