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

contestada

Respuesta :

jmonterrozar jmonterrozar · Answer 1 · 2020-07-05T03:44:02+02:00

Answer:

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

andromache andromache · Answer 2 · 2022-03-03T12:27:37+01:00

The calculation of each of the probabilities should be shown below.

Following formulas should be used

from binomial distibution: P (X = x) = [tex](nCx) \times (p) x \times (1-p) n-x[/tex]

from normal distribution: P (X <= x) =[tex](x-np) \div \sqrt T (np (1-p))[/tex]

Since, n = 25 and p (0.5, 0.6, 0.8),

So, the probabilities are:

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

learn more about probability here: https://brainly.com/question/15944614