## Essentials of Statistics (5th Edition)

a)$z=\frac{value-mean}{standard \ deviation}=\frac{2500-3369}{567}=-1.53.$ Using the table, the probability of z being less than -1.53 is: 0.0630. b)By using the table, the z-score corresponding to 10%=0.1: z=-1.28. Hence the corresponding value:$mean+z⋅standard \ deviation=3369−1.28⋅567\approx2642.$ c)$z=\frac{value-mean}{standard \ deviation}=\frac{1500-3369}{567}=-3.3.$ Using the table, the probability of z being less than -3.3 is: 0.0005. d)$z=\frac{value-mean}{standard \ deviation}=\frac{3400-3369}{567/\sqrt {25}}=0.27.$ Using the table, the probability of z being more than 0.27 is 1 minus z being less than 0.27 is, hence the probability: 1-0.6064=0.3936.