math stisctic 245

20. Some experts label a "genius" as one who has an IQ score of more than 140. Approximately 0.4% of the population has an IQ score more than 140. What is the probability that in a random class of 25 first grade students at least one of them would be labeled "genius"? (10 points) 1. A box of Apple Jacks is advertised to weigh 11 ounces. The weights are normally distributed with a mean weight of 1 1 ounces and standard deviation of .4 ounce. For a box of Apple Jacks selected at random, find the probability that: a. it weighs more than 12 ounces (5 points) b. it weighs less than 10 1/2 ounces (5 points) c. If you randomly selected 25 boxes of Apple Jacks, what is the probability that the mean weight of these boxes would be less than 10 % oz.? (6 points)