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Answer:
<em> The probability that x is between 60 and 110.</em>
<em>P(60 < x<110) = 0.6436</em>
Step-by-step explanation:
<u><em>Step( i )</em></u> :-
Given data the random variable 'X' will have a distribution that is approximately normal with mean μ = 83 and standard deviation σ = 27.
<em>Mean of the Population 'μ' = 83</em>
<em>Standard deviation of the Population 'σ' = 27.</em>
<u><em>Step(ii):-</em></u>
Given X =60
<u><em>Step(iii):-</em></u>
<em>Given X = 110</em>
The Probability that between 60 and 110
<em>P(60 < x<110) = P( -0.851 < z< 1)</em>
<em> = P( Z≤1) - P(Z≤ -0.851)</em>
= (0.5 + A(1)) - (0.5- A(-0.851))
= (0.5 +0.3413)- (0.5 - 0.3023) ( check normal table yellow mark)
= 0.8413 - 0.1977
P(60 < x<110) = 0.6436
<u><em>Final answer</em></u>:-
<em> The probability that x is between 60 and 110.</em>
<em>P(60 < x<110) = 0.6436</em>
<em> </em>
