Calculate a normal tail probability and a two-person combined probability.

Calculate a normal tail probability and a two-person combined probability.

8 marks
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Residents of a small town have savings which are normally distributed with a mean of \(3000 and a standard deviation of $500. (i) What percentage of townspeople have savings greater than \)3200? (ii) Two townspeople are chosen at random. What is the probability that both of them have savings between \(2300 and \)3300? (iii) The percentage of townspeople with savings less than d dollars is 74.22%. Find the value of d.[8]

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Answer:Since \(z_{0.7422}=0.65\), \(d=3000+500(0.65)=\$3325\).

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