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Find z_(alpha//2) for alpha=0.13.
z_(alpha//2)=◻ (Round to two decimal places as needed.)

Find zα/2 z_{\alpha / 2} for α=0.13 \alpha=0.13 .\newlinezα/2= \mathrm{z}_{\alpha / 2}=\square (Round to two decimal places as needed.)

Full solution

Q. Find zα/2 z_{\alpha / 2} for α=0.13 \alpha=0.13 .\newlinezα/2= \mathrm{z}_{\alpha / 2}=\square (Round to two decimal places as needed.)
  1. Understand the problem: Understand the problem.\newlineWe need to find the z-score zα/2z_{\alpha/2} that corresponds to an alpha level of 0.130.13 for a two-tailed test. This means we are looking for the z-score where the area in each tail of the standard normal distribution is 0.13/20.13/2, since the total area for both tails must add up to α\alpha.
  2. Calculate α/2\alpha/2: Calculate α/2\alpha/2.\newlineTo find the z-score for the two-tailed test, we first need to divide α\alpha by 22 because the alpha level is split between the two tails of the distribution.\newlineα/2=0.13/2=0.065\alpha/2 = 0.13 / 2 = 0.065
  3. Use z-table: Use the standard normal distribution table.\newlineWe will use the standard normal distribution table (z-table) to find the z-score that corresponds to an area of 0.0650.065 to the left of the z-score. Since the table typically gives the area to the left of the z-score, we need to find the value that corresponds to 10.065=0.9351 - 0.065 = 0.935, because we want the area in the right tail to be 0.0650.065.
  4. Find z-score: Find the z-score from the table.\newlineLooking at the z-table, we find the closest area to 0.9350.935 and then identify the corresponding z-score. The z-score that corresponds to an area of 0.9350.935 is approximately 1.511.51.
  5. Round z-score: Round the z-score to two decimal places.\newlineThe z-score we found is already at two decimal places, so no further rounding is necessary.\newlinezα/2=1.51z_{\alpha/2} = 1.51

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