Standard Normanl Drill:
A. Find the number z such that the proportion of observations that are less than z in a standard Normal distribution is 0.8.
B. Find the number z such that 35% of all observations from a standard Normal distribution are greater than z.
i have now idea what they are asking, any help?
Ah, the mysterious world of statistics! Don't worry, I'll do my best to make it less confusing with a touch of humor.
A. To find the number "z" in a standard Normal distribution where 0.8 (or 80%) of the observations are less than "z," think of it as finding the life of the party! You're searching for the value where 80% of the guests are more reserved and chill than that number. So, let's just say "z" is that hipster guest who's more introverted than 80% of the crowd.
B. Now, imagine you're at a party where 35% of all people are greater than "z." In this case, "z" is like that popular person who outshines 35% of the entire gathering. They're like the talk of the party, attracting all the attention! So, you're looking for that "z" who stands out in the crowd.
Hope my quirky explanations help make sense of the questions. Just remember, in life, and statistics, there's always a hidden punchline waiting to be discovered!
Of course! Let's break down both parts of the question and explain how to solve them:
A. Find the number z such that the proportion of observations that are less than z in a standard Normal distribution is 0.8.
To solve this, we need to find the z-score corresponding to a cumulative probability of 0.8 in a standard Normal distribution. The z-score represents the number of standard deviations an observation is away from the mean.
To find the answer, you can use a standard Normal distribution table (also known as a z-table) or a calculator with built-in statistical functions. These tools will allow you to look up or calculate the z-value for a given probability.
1. Using a z-table: Locate the value closest to 0.8 in the body of the table. The row headers represent the tenths digit, and the column headers represent the hundredths digit. The intersection of these values will give you the z-score.
2. Using a calculator: Many calculators or statistical software have functions to find the z-score directly. You can input the probability of 0.8 and obtain the corresponding z-value.
Once you have the z-score, you can apply it to the mean and standard deviation of the standard Normal distribution to find the corresponding value, z.
B. Find the number z such that 35% of all observations from a standard Normal distribution are greater than z.
Similar to part A, we need to find the z-score corresponding to a cumulative probability. However, this time we are interested in the proportion of observations that are greater than z, rather than less than z.
To solve this, you can follow the same steps as in part A, but with a slight modification. Instead of looking up the probability in the z-table or calculator, you need to find the probability of the area to the left of z. Subtract this probability from 1, and you will obtain the proportion of observations greater than z. Next, equate this proportion to 0.35 (since we want 35% of observations to be greater than z) and solve for z using the z-table or calculator.
By applying these steps, you should be able to find the answers to both parts of the question.
It helps to know how to read a z-table to answer these kinds of questions.
For part A, you will need to find a z value where 80% is below the z and 20% is above the z. Remember that the mean divides the distribution in half: 50% is below the mean and 50% is above the mean. Therefore, 80% is above the mean and you will have to look within the table at .30 (most tables go out to 4 places after the decimal point, so the table might show .3000) or closest to that value to find the z if your table shows from mean to z values. Tables can be set up differently, so be mindful of that when you look for these values.
For part B, you will need to find a z value where 65% is below the z and 35% is above the z. Therefore, in a table that shows from mean to z values, you will look for .15 (or .1500) in the table to find the z.
Both z values will be positive because they are above the mean of the distribution. (Negative z values are below the mean of the distribution.)
I hope this will help.