Assignment 3.2 Central Limit Theorem

Assignment 3.2 Central Limit Theorem - To resolve this I...

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To resolve this I will start by finding out how many standard deviations is the value from the mean using the formula Z = X µ σ and the result of this is approximately 0.67 standard deviations from the mean. After that we can say that P(male > 70”) = P(Z > 0.67). Then using the table 5 from the text book we have that for Z = 0.67 the value is 0.7486. Then by subtracting the area under the curve minus the value for Z = 0.67 we will have the area above Z = 0.67 which is 0.2514 which represents a 25.14% probability of randomly getting a male taller than 70”. For this part of the exercise I will use the same reasoning used in the prior bullet, the only modification that I will do is use the standard error instead of using the regular standard deviation in the Z formula. The standard error is calculated by the formula σ x = σ n . After the calculation we have that Z ≈ 2.11. The value Z = 2.11 in the table is 0.9826. Then 1 – 0.9826 = 0.0174, which represent a 1.74% probability of the average height for these 18-year-old males is more than 70 inches.
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