Question

For which of the following binormial distributions are the conditions for the normal approximation to the binomial distribution satisfied?

a. = 40, |
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b. = 400, |
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c. = 20, |
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d. = 20, |

Answer #1

For normal approximation to binomial, np > 5 and nq >5

a) n = 40

p - 0.9

q = 1 - 0.9 = 0.1

nq = 40x0.1 = 4

Conditions for normal approximation are not satisfied.

b) n = 400,

p = 0.99

q = 1 - 0.99 = 0.01

nq = 400x0.01 = 4

Conditions for normal approximation are not satisfied.

c) n = 20

p = 0.2

q = 1 - 0.2 = 0.8

np = 20x0.2 = 4

Conditions for normal approximation are not satisfied.

d) n = 20

p = 0.3

q = 1 - 0.3 = 0.7

np = 20x0.3 = 6

nq = 20x0.7 = 14

Both np and nq > 5

So, **Conditions for normal approximation are
satisfied**

**Ans: d) n = 20, p = 0.3**

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