Problem
I. Suppose that weights of bags of potato chips coming from a factory follow a normal distribution with a mean of 12.5 ounces and a standard deviation of 0.3 ounces. How likely are you to sample a bag at random that weights more than 13 oz?
II. Mensa is an international society whose membership is limited to persons having IQ's above the general population's 98th percentile. It is known that the average IQ for the general population is 100, the standard deviation is 16, and the distribution is normal. What, then, is the lowest IQ that will qualify a person to belong to Mensa?
III. Dental structure provides an effective criterion for classifying certain fossils. Not long ago a baboon skull of unknown origin was discovered in a cave in Angola; its third-molar length was 9.0 mm. Speculation arose that the baboon in question might be a "missing link" and belong to the genus Papio. Members of this genus have third molars that measure, on the average, 8.18 mm long with a standard deviation of 0.47 mm.
i. What is the z-score of the 9.0 mm molar?
ii. What percentage of Papio baboons would have a third molar this long or longer?
iii. Do you think it likely that the molar comes from a Papio baboon?