The graph illustrates a normal distribution for the prices paid for a particular model of HD television. The price paid is 1600 and the standard deviation is 55
What is the approximate percentage of buyers who paid more than 1710 ?
I got 2.28 and it is wrong
What is the approximate percentage of buyers who paid more than $1763?
I got 0.1% it is wrong
What is the approximate percentage of buyers who paid between $1600 and $1710?
I got 47.7% it is wrong
What is the approximate percentage of buyers who paid between $1600 and $1765
I got 49.87% and it is correct
What is the approximate percentage of buyers who paid between $1600 and $1665
I got 34.1% And it’s wrong
What is the approximate percentage of buyers who paid between $1545 and $1655
I got 68.2% And it is wrong
Please help I don’t know how it is wrong
What is the approximate percentage of buyers who paid more than 1710 ?
I got 2.28 and it is wrong
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I put in mean = 1600
sigma = 55
more than 1710
click on recalulate
.0152 or 1.52 percent
http://davidmlane.com/hyperstat/z_table.html
I used that and the answers are incorrect
To solve these questions, we can use the concept of z-scores. A z-score measures the deviation of a particular value from the mean in terms of standard deviations.
First, we need to convert the given prices to z-scores using the formula:
z = (x - μ) / σ
where:
- z is the z-score
- x is the given value
- μ is the mean of the distribution
- σ is the standard deviation of the distribution
For the given problem, we have:
- Price paid: 1600
- Standard deviation: 55
Now, let's solve each question step by step:
1. What is the approximate percentage of buyers who paid more than $1710?
To answer this, we need to find the area under the curve to the right of $1710, which represents the percentage of buyers who paid more than $1710.
First, we calculate the z-score for $1710:
z = (1710 - 1600) / 55 ≈ 2
Now, we look up the corresponding z-score (2) in the standard normal distribution table, or use a calculator with a built-in function like "normdist" or "normsdist". The table or calculator will give us the area to the left of the z-score. Let's denote this as P(Z ≤ 2).
Since we need the area to the right of the z-score, we subtract P(Z ≤ 2) from 1. This gives us the approximate percentage of buyers who paid more than $1710.
Answer: The approximate percentage of buyers who paid more than $1710 can be calculated as 1 - P(Z ≤ 2).
2. What is the approximate percentage of buyers who paid more than $1763?
Again, we calculate the z-score for $1763:
z = (1763 - 1600) / 55
After calculating the z-score, we follow the same steps as in the previous question to find the approximate percentage of buyers who paid more than $1763.
Answer: The approximate percentage of buyers who paid more than $1763 can be calculated as 1 - P(Z ≤ z).
3. What is the approximate percentage of buyers who paid between $1600 and $1710?
To find the percentage of buyers who paid between $1600 and $1710, we need to find the area under the curve between these two values.
First, we calculate the z-scores for both prices:
z1 = (1600 - 1600) / 55 ≈ 0 (the mean has a z-score of 0)
z2 = (1710 - 1600) / 55
Next, we find the area to the left of z2 in the standard normal distribution table or using a calculator. Let's denote this as P(Z ≤ z2).
To find the percentage of buyers who paid between these two values, take the difference between P(Z ≤ z2) and P(Z ≤ 0).
Answer: The approximate percentage of buyers who paid between $1600 and $1710 can be calculated as P(Z ≤ z2) - P(Z ≤ 0).
4. What is the approximate percentage of buyers who paid between $1600 and $1765?
To find the percentage of buyers who paid between $1600 and $1765, we follow the same steps as in the previous question, but this time we calculate the z-score for $1765.
Answer: The approximate percentage of buyers who paid between $1600 and $1765 can be calculated as P(Z ≤ z3) - P(Z ≤ 0), where z3 is the z-score for $1765.
5. What is the approximate percentage of buyers who paid between $1600 and $1665?
Similarly, we calculate the z-score for $1665:
z = (1665 - 1600) / 55
Again, follow the same steps as in the previous questions.
Answer: The approximate percentage of buyers who paid between $1600 and $1665 can be calculated as P(Z ≤ z4) - P(Z ≤ 0), where z4 is the z-score for $1665.
6. What is the approximate percentage of buyers who paid between $1545 and $1655?
Lastly, we calculate the z-scores for $1545 and $1655:
z5 = (1545 - 1600) / 55
z6 = (1655 - 1600) / 55
Follow the same steps as before to find the percentage of buyers who paid between these two values.
Answer: The approximate percentage of buyers who paid between $1545 and $1655 can be calculated as P(Z ≤ z5) - P(Z ≤ z6).
Remember to refer to a standard normal distribution table or use a calculator with appropriate functions to find the values of P(Z ≤ z).