he random variable X has a binomial distribution with n = 10 and p = 0.03. Deter

Question

he random variable X has a binomial distribution with n = 10 and p = 0.03. Determine the following probabilities. Round your answers to six decimal places (e.g. 98.765432). (a) Upper P left-parenthesis Upper X equals 5 right-parenthesis equals (b) Upper P left-parenthesis Upper X less-than-or-equal-to 2 right-parenthesis equals (c) Upper P left-parenthesis Upper X greater-than-or-equal-to 9 right-parenthesis equals (d) Upper P left-parenthesis 3 less-than-or-equal-to Upper X less-than 5 right-parenthesis equals

Explanation / Answer

n = 10, p = 0.03, q = 1 - p = 0.97

P(x) = nCx p^x q^(n - x)

(a) P(5) = 10C5 0.03^5 0.97^5 = 0.000005

(b) P(x 2) = P(0) + P(1) + P(2) = 10C0 0.03^0 0.97^10 + 10C1 0.03^1 0.97^9 + 10C2 0.03^2 0.97^8

= 0.997235

(c) P(x 9) = P(9) + P(10) = 10C9 0.03^9 0.97^1 + 10C10 0.03^10 0.97^0 = 0.000000

(d) P(3 x 5) = P(3) + P(4) + P(5) = 10C3 0.03^3 0.97^7 + 10C4 0.03^4 0.97^6 + 10C5 0.03^5 0.97^5

= 0.002765

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