Let X have a binomial distribution with parametersn = 25and p. Calculate each of the following probabilities using the normal approximation (with the continuity correction) for the casesp = 0.5, 0.6, and 0.8and compare to the exact binomial probabilities calculated directly from the formula forb (x; n, p). (Round your answers to four decimal places.) (a) P (15 ≤ X ≤ 20)

Question

Mathematics

Livia Waller

16 September, 20:48

Let X have a binomial distribution with parametersn = 25and p. Calculate each of the following probabilities using the normal approximation (with the continuity correction) for the casesp = 0.5, 0.6, and 0.8and compare to the exact binomial probabilities calculated directly from the formula forb (x; n, p). (Round your answers to four decimal places.) (a) P (15 ≤ X ≤ 20)

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Akira · Answer 1

The answer is explained below

Step-by-step explanation:

We have the following formulas:

from binomial distibution: P (X = x) = (nCx) * (p) x * (1-p) n-x

from normal distribution: P (X < = x) = (x-np) / sqrT (np (1-p))

Now, n = 25 and p (0.5, 0.6, 0.8), we replace in the formulas and we are left with the following table:

P P (15<=X<=20) P (14.5<=X<=20.5)

0.5 0.2117 is less than 0.2112

0.6 0.5763 is less than 0.5685

0.8 0.5738 is greater than 0.5957