Question: Charles, Julia, and Alex are in grades 4, 3, and 2, respectively, and are representing their school at a spelling bee. The school's team score is the sum of the number of words the individual students spell correctly out of 50 words each. Different words are given for each grade level. From practicing at school, it is known that the probability of spelling each word correctly is .9 for Charles and .8 for the younger two, Julia and Alex.
a. Find the mean and standard deviation for the number of correct words for each child.
b. Find the mean and standard deviation for the team score.
c. Assume that the individual scores are independent. Does the team score have a binomial distribution? Explain.
d. Although not obvious from the material in this chapter, the team score would be approximately normal with the mean and standard deviation you were asked to find in part (b). If last year's team score was 131, what is the approximate probability that this year's team scores as well or better?