Using Normal Approximation in Probability Calculations with Binomial Distribution
- np ≥ 10
- n(1 - p) ≥ 10
- np = 202 * 0.47 ≈ 94.94
- n(1 - p) = 202 * (1 - 0.47) ≈ 107.06
To proceed with probability calculations using the normal approximation, we can make continuity corrections by adding or subtracting 0.5 from each value.
Calculating Probabilities:
Using normal approximation with continuity correction:
z = (81 + 0.5 - 94.94) / 50.32 ≈ -0.2772
p(x ≤ 98):Using normal approximation with continuity correction:
z = (98 + 0.5 - 94.94) / 50.32 ≈ 0.0636
p(x < 70):Using normal approximation with continuity correction:
z = (70 - 0.5 - 94.94) / 50.32 ≈ -0.5014
p(x ≥ 105):Using normal approximation with continuity correction:
z = (105 + 0.5 - 94.94) / 50.32 ≈ 0.2057
p(x > 104):Using normal approximation with continuity correction:
z = (104 - 0.5 - 94.94) / 50.32 ≈ 0.2257