Answer
a) Too high.
b)5.5524 and 5.7876
Work Step by Step
a)$z=\frac{value-mean}{standard \ deviation}=\frac{5.7-5.67}{0.06}=0.5.$
$z=\frac{value-mean}{standard \ deviation}=\frac{5.64-5.67}{0.06}=-0.5.$
By using the table the corresponding probability: 0.6915-0.3085=0.3830=38.3%. Hence 100%-38.3%=61.7% is rejected, which is too high, it is more than half of the legal quarters.
b)By using the table, the z-score corresponding to 0.025 and 0.975: z=$\pm 1.645$. Hence the corresponding values:$mean+z⋅standard \ deviation=5.67-1.96⋅0.06=5.5524.$
$mean+z⋅standard \ deviation=5.67+1.96⋅0.06=5.7876.$
