Elementary Statistics (12th Edition)

a)$z=\frac{value-mean}{standard \ deviation}=\frac{2-1.184}{0.587}=1.39$. By using the table the corresponding probability: 0.9177=91.77%. b)$z=\frac{value-mean}{standard \ deviation}=\frac{4-1.184}{0.587}=4.8$. By using the table the corresponding probability: 1-0.9999=0.0001=0.01%. c)By using the table, the z-score corresponding to 1-0.05=0.95: z=1.645. Hence the corresponding value:$mean+z⋅standard \ deviation=1.184+1.645⋅0.587=2.15.$ Hence not all earthquakes above the 95th percentile will cause indoor items to shake, because it is less than 4.