When we know population data, but have a sample to work with, we use the formula above to compute a Z score.
Solution :
Given that,
mean = = 200
standard deviation = = 25
_{} = / n = 25 / 49 = 3.5714
= P[(190 - 200) / 3.5714 < ( - _{}) / _{} < (205 - 200) / 3.5714)]
= P(-2.8 < Z < 1.4)
= P(Z < 1.4) - P(Z < -2.8)
= 0.9192 - 0.0026
Probability = 0.9166
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