In Scotland in November on average 80% of days are cloudy. Assume that the weather on any one day is independent of the weather on other days. (i) use normal approximation to find the probability of there being fewer than 25 cloudy days in Scotland in Novermber (30 days).
First find the z-score of 80%. The mean is 24, as it asks for the probably of fewer than 25 days being cloudy out of 30. 24 is 80% of 30. The number of days in question is 24. The standard deviation is 2.19 (variance=4.8). Use the z-score formula to figure out the probability. |dw:1366002612527:dw| z=24.5 - 24/2.19 (use the continuity correction of +.5 to account for all numbers) z=.228 On the z-table, find look under each column to find the numbers that make up .228. You should find .5902. This is the probability of fewer than 25 days being cloudy. The answer is .590.