Assume that a normal distribution has a mean of 21 and a standard deviation of 2.
Use the empirical rule to find the percentage of values that lie above 23.
Now I did this on the Ti 83 by using Normalcdf(-5,1) and getting an answer of 0.84 and then 1-0.84 and I get about 15.9 in percentage but it is showing me wrong.
Help me I am confused.
Where am I going wrong?
assume that a normal distribution of data has a mean of 19 and a standard deviation of 4. Use the 68-95-99.7 rule to find the percentage of values that lie above 31.
To find the percentage of values that lie above a certain value using the empirical rule, you need to use the concept of standard deviations.
First, calculate the z-score for the value 23 using the formula:
z = (x - μ) / σ
where x is the value we're interested in, μ is the mean of the distribution, and σ is the standard deviation.
In this case, x = 23, μ = 21, and σ = 2, so the z-score is:
z = (23 - 21) / 2 = 1
The z-score tells you how many standard deviations a value is from the mean. In this case, 23 is one standard deviation above the mean.
Now, we can use the empirical rule to estimate the percentage of values above 23. The empirical rule states that for a normal distribution, approximately 68% of values lie within one standard deviation of the mean, 95% lie within two standard deviations, and 99.7% lie within three standard deviations.
Since 23 is one standard deviation above the mean, we know that approximately 68% - 34% = 34% of values lie above it.
Therefore, the percentage of values that lie above 23 is approximately 34%.
Now, let's verify if your calculation using the Ti 83 is correct.
The Normalcdf function on the Ti 83 calculates the area under the normal curve between two z-scores. To find the area above a certain z-score, you need to subtract the result from 1.
In this case, you calculated Normalcdf(-5, 1) on your Ti 83. However, to find the area above 1, you should calculate Normalcdf(1, ∞).
Finding Normalcdf(1, ∞) using a calculator or a statistical software will give you the correct percentage of values above 23, which is approximately 15.87%.
So it seems like you made a small mistake in your calculation.