Question

Seattle, Washington, averages μ = 34 of annual precipitation. Assuming that the distribution of precipitation amounts is approximately normal with a standard deviation of σ = 6.5, determine whether each of the following represents a fairly typical year, an extremely wet year, or an extremely dry year. Annual precipitation of 41.8 inches Annual precipitation of 49.6 inches Annual precipitation of 28.0 inches

Answer 1

since an absolute z score value of 2 or more considered to be extreme

a)

z score for Annual precipitation of 41.8 inches =(X-mean)/standard deviation =(41.8-34)/6.5=1.2

since this is not unusual value , this should be considered as a typical year

b)

z score for Annual precipitation of 49.6 inches =(X-mean)/standard deviation =(49.6-34)/6.5=2.4

since the value is higher than 2, this should be considered as extremely wet year,

c)

z score for Annual precipitation of 28 inches =(X-mean)/standard deviation =(28-34)/6.5=-0.92

since this value is not below z score of -2 , this should not be considered as a typical year