The age distribution of householders is an important tool for marketer interested in providing age-appropriate advertising for the particular product they wish to market.  A study conducted by the Joint Center for Housing Studies estimates that, in 1995, 31% of all householders will be between 45 and 64.  Suppose a sample of 500 is taken in 1995. (Hint: use the normal approximation to the binomial.)

a) What is the probability that fewer than 135 householders will be between 45 and 64?

b) What is the probability that between 135 and 180 householders inclusive will be between 45 and 64?

(Can you also explain how you got the answer)

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