2. Of the 270 numbers you collected last week, 92 started with the digit 1. I th

Question

2. Of the 270 numbers you collected last week, 92 started with the digit 1. I think that each digit should be equally likely to be the first digit, so the digit 1 should be the first digit exactly of the time. Assume that our numbers represent a random sample. a) Estimate the probability of 92 or more of the first digits being 1 using a normal approximation. b) Calculate the probability of 92 or more of the first digits being a 1 using a binomial cumulative distribution function (on a computer or calculator)

Explanation / Answer

n = 272

a) x = 1/9 * 270 = 30

SD = sqrt(30 * 8/9) = 5.16

z = (92 - 30)/5.16

z = 12.02

P = 0.000

b) Binomial:

P(X > 92)  < 0.000001

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