Solved on Mar 12, 2024
Find the -score where the area to its right under the standard normal distribution is 0.39. Round the answer to 4 decimal places.
STEP 1
Assumptions
1. The standard normal distribution is symmetric about the mean, which is 0.
2. The total area under the standard normal distribution curve is 1.
3. The -score is the number of standard deviations a data point is from the mean.
4. The area to the right of the -score under the standard normal distribution is given as 0.39.
5. We are looking for the -score such that the area to the left of it is .
STEP 2
To find the -score corresponding to a given area to the left, we use the inverse of the standard normal cumulative distribution function (CDF), often denoted as .
STEP 3
Calculate the area to the left of the -score, which is .
STEP 4
Use a standard normal distribution table, calculator, or statistical software to find the -score that corresponds to the area to the left of 0.61.
If using a table, we look for the value closest to 0.61 in the table and then find the corresponding -score. If using a calculator or software, we input the area to the left into the inverse CDF function.
STEP 5
After finding the -score using one of the methods in STEP_4, we round the answer to four decimal places as requested.
The -score such that the area to its right under the standard normal distribution is 0.39 is approximately .
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