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)

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

b

step-by-step explanation: