Let X have a binomial distribution with parameters
n = 25
and p. Calculate each of the following probabilitiesusing the normal approximation (with the continuity correction) forthe cases
p = 0.5, 0.6, and 0.8
and compare to the exact binomial probabilities calculateddirectly from the formula for
b(x; n, p).
(Round your answers to four decimal places.)
(a)
P(15 ≤ X ≤ 20)
| p | P(15 ≤ X ≤ 20) | P(14.5 ≤ Normal ≤ 20.5) |
|---|
| 0.5 | 1 | 2 |
| 0.6 | 3 | 4 |
| 0.8 | 5 | 6 |
(b)
P(X ≤ 15)
| p | P(X ≤ 15) | P(Normal ≤ 15.5) |
|---|
| 0.5 | 10 | 11 |
| 0.6 | 12 | 13 |
| 0.8 | 14 | 15 |
(c)
P(20 ≤ X)
| p | P(20 ≤ X) | P(19.5 ≤ Normal) |
|---|
| 0.5 | 19 | 20 |
| 0.6 | 21 | 22 |
| 0.8 | 23 | 24 |
