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please use a TI 84 calculator and explain how you solved the following question membership into...

please use a TI 84 calculator and explain how you solved the following question

membership into the math syndicate requires a score over 220 on a special examination. Nine candidates take test, and their summary results indictate that tehir mean score is 225. This special math exam is known to have scores that are normally distributed with a mean of 165 and a standard deviation of 25.

a) if one person is randomly selected from the general population, find the probability of getting someone with a score of at least 220.

b) if nine people are randomly selected from the general population, find the probability that their mean score is at least 220.

c) although the summary results are available, the individual IQ test scores have been lost. Can it be concluded that all 9 candidates have a score above 220, so that they are all eligible for the syndicate? can we conclude that anyone of the nine is eligible? explain.

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Sol X= scores XN Nl M=165 = 25) a) P[x3,220] = P(x-4 = 220-1657 25 > P[ 22 2-2] > 0.0139 na b) Pl X 3,2207 = P xq=165 Plz 3,

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