Find the number z (± 0.01) such that the proportion of observations that are less than z in a standard Normal distribution is 0.8
Find the number z (± 0.01) such that 59% of all observations from a standard Normal distribution are greater than z
It would help if you proofread your questions before you posted them. Your questions are not clear. I do not understand what you are asking.
I posted this question straight from the quiz, so I'm not sure why you're confused.
To find the number 'z' in both cases, we need to utilize the concept of the standard normal distribution and its associated Z-scores.
For the first case:
Step 1: Identify the given proportion as 0.8. This means that 80% of the observations in a standard normal distribution are less than 'z'.
Step 2: Convert the proportion to the corresponding Z-score using a standard normal distribution table or a statistical calculator. The Z-score associated with a proportion of 0.8 is approximately 0.84.
Step 3: Calculate the actual value of 'z' by multiplying the Z-score by the standard deviation of the standard normal distribution, which is 1. In this case, z = 0.84 * 1 = 0.84.
Therefore, the number 'z' for which the proportion of observations that are less than z in a standard normal distribution is 0.8 is approximately 0.84 (± 0.01).
For the second case:
Step 1: Identify the given proportion as 0.59. This means that 59% of the observations in a standard normal distribution are greater than 'z'.
Step 2: Subtract the given proportion from 1 to find the proportion of observations that are less than 'z'. In this case, 1 - 0.59 = 0.41.
Step 3: Convert the proportion to the corresponding Z-score using a standard normal distribution table or a statistical calculator. The Z-score associated with a proportion of 0.41 is approximately -0.27.
Step 4: Calculate the actual value of 'z' by multiplying the Z-score by the standard deviation of the standard normal distribution, which is 1. In this case, z = -0.27 * 1 = -0.27.
Therefore, the number 'z' for which 59% of all observations from a standard normal distribution are greater than z is approximately -0.27 (± 0.01).