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The critical value, z(α), is found using a standard normal distribution table. In this case, z(0.01) is given as 1.28. How is this value determined?

a. By solving a quadratic equation
b. Consulting a standard normal distribution table
c. Using calculus to find the area under the curve
d. Employing a statistical software algorithm

User Amrods
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Final answer:

The critical value z(0.01) is found by consulting a standard normal distribution table or using statistical software, which calculates the related area under the curve to determine the z-score that has an area of 0.99 to the left of it.

Step-by-step explanation:

The value z(0.01) is typically determined by consulting a standard normal distribution table or employing statistical software. These tables or software calculate the area under the standard normal curve, which is a bell-shaped curve representing the normal distribution with a mean of 0 and a standard deviation of 1. The critical value, in this case, z(0.01), corresponds to the z-score that has an area of 0.99 to the left of it under the normal curve, leaving an area of 0.01 to the right. This z-score marks the point beyond which the tail accounts for 1% of the distribution. The process involves finding the z-score associated with the cumulative probability of 0.99. The exact value can vary based on the reference source but is usually around 2.326. For example, a critical value of 1.645 associated with a confidence level of 90% means that 1.645 standard deviations from the mean in either direction on the normal curve will include the central 90% of the data.

User Esteban Collado
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