Sampling Distribution of a Proportion (4 of 4)
Next section: Difference between proportions
Therefore to compute the probability of 10 or more successes, compute the
area above 9.5 successes. In terms of proportions, 9.5 successes is 9.5/20
= 0.475. Therefore, 9.5 = (0.475 - 0.40)/.11 = 0.682 standard deviations
above the mean. The probability of being 0.682 or more standard deviations
above the mean is 0.247 rather than the 0.182 that was obtained previously.The
exact answer calculated using the
binomial distribution
is 0.245. For small sample sizes the correction can make a much bigger difference
than it did here.
Next section: Difference between proportions