The central limit theorem states that ifY1, Y2, ..., Ynare a sequence of random variables that are independent and identically distributedwithE[Y;] = µV[Y;] = o²for each i (with both of those quantities being finite), andΣΥ= -ni=1is the sample mean random variable, when n is large, we can approximate thedistribution of the sample mean asYn ~ Normal(u, o²In)and also approximate the distribution of the sumnSnΣΗi=1asSn - Normal(nu, no²).Question: Suppose that a fair coin is tossed 180 times with the results of the tossesregarded as independent events. Use the central limit theorem to approximate theprobability that the total number of heads obtained is greater than 97.• use the Normal probability tables to look up the probability• the table can be used for arguments specified up to 2 decimal places, soround your argument appropriately• do not use a continuity correction.

# Given : x be the no of heads obtained after tossing a fair coin 180 times .then using central…

Answered: Question: Suppose that a fair coin is…

A First Course in Probability (10th Edition)

10th Edition

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Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question: Suppose that a fair coin is tossed 180 times with the results of the tosses regarded as independent events. Use the central limit theorem to approximate the probability that the total number of heads obtained is greater than 97. Uco tho Normal pro hility tables to leek the prebabilihy