Give FULL step by step solutions with formulas and explanation. Topic: The Normal Distribution [Book: John R. Taylor - Introduction to Error Analysis..]

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5.21. * * The Giraffe Club of Casterbridge is a club for young adults (18-24 years) who are unusually tall. There are 2,000 women between the ages of 18 and 24 in Casterbridge, and the heights of women in this age range are distributed normally with a mean of 5'51/2" and standard deviation of 21/2". (a) If the Giraffe Club initially sets its minimum height for women at 5'10", approximately how many women are eligible to join? (b) A year or so later, the club decides to double its female membership by lowering the minimum height requirement; what would you recommend that the club set as its new minimum height for women (to the nearest half inch)