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Answer:
C) 53.3%
The probability that a data value is between 206 and 230
P( 206 ≤X≤230) = 0.5328 = 53.3%
Step-by-step explanation:
<u><em>Explanation</em></u>
<em>Given that Mean of the Normal distribution(μ) = 222</em>
Given that the standard deviation of the Normal distribution (σ) = 16
Let 'X' be the random variable in the Normal distribution
<em>we have to find that the probability that a data value is between 206 and 230</em>
<u><em>solution:-</em></u>
<u><em>Step(i):-</em></u>
Let 'X' = 206
Let X = 230
<u><em>Step(ii):-</em></u>
The probability that a data value is between 206 and 230
P( 206 ≤X≤230) = P( -1≤Z≤0.5)
= |A(0.5)+A(-1)|
= 0.1915+0.3413
= 0.5328
<u><em>final answer:-</em></u>
<em>The probability that a data value is between 206 and 230</em>
<em>P( 206 ≤X≤230) = 0.5328 = 53.3%</em>