Toyzz, Inc is releasing a new action figure, Normal-Man! The biggest issue with Normal-Man is that his dimensioning needs to be just right or else he is terrifying to children. Toyzz, Inc. has worked carefully with a factory to reduce variability in size of the action figures as the come off the assembly line. A random sampling of the action figures has been measured and they follow an approximately normal distribution with mean height 46.42 cm and the standard deviation of 0.09 cm. Research has shown that anything taller than 46.62 cm or shorter than 46.31 cm is terrifying!

1) What percentage of the action figures are currently terrifying?

2) Since the action figures follow an approximately normal distribution, what height would you suggest the factory sets as it's target mean height?

3) Using your new mean and the same standard deviation, no what percent of the action figures are terrifying?

4) If you wanted no more than 3.4% of action figures to be terrifyingly short (after the new mean has been set), how tall would the action figures need to be?