The population mean length of a hospital stay for surgery is 5.5 days and the standard deviation is 1.9 days. What percentage of patients are hospitalized for 3.9 days or less?
I've read the book and looked at the explanation that it gives and it's not making any sense.
3.9 days is 2.05 std from the mean.
Look that up in your Z table.
Just use the left tail value.
What does that mean? What's a Z table and what does std mean?
http://en.wikipedia.org/wiki/Standard_normal_table
http://www.mathworks.com/help/matlab/ref/std.html
To calculate the percentage of patients hospitalized for 3.9 days or less, we need to use the normal distribution and the z-score.
1. Calculate the z-score:
The z-score shows how many standard deviations a specific value is from the mean. We can calculate the z-score using the formula:
z = (x - μ) / σ
where
x = 3.9 (number of days),
μ = 5.5 (population mean of hospital stay),
σ = 1.9 (standard deviation).
Substituting the values, we get:
z = (3.9 - 5.5) / 1.9 ≈ -0.842.
2. Look up the z-score in the standard normal distribution table:
Using a standard normal distribution table or a calculator, find the corresponding area or percentage for the z-score obtained in the previous step. In this case, the area to the left of z = -0.842 is approximately 0.2001.
3. Interpret the result:
Since we are interested in the percentage of patients hospitalized for 3.9 days or less, we need to find the area to the left of the z-score. This represents the percentage of patients with a hospital stay less than or equal to 3.9 days.
To get the final percentage, we convert the decimal to a percentage by multiplying it by 100:
0.2001 * 100 ≈ 20.01%.
Therefore, approximately 20.01% of patients are hospitalized for 3.9 days or less.
If the explanation in your book is not making sense, it might be helpful to review the concepts of the normal distribution, z-scores, and the process for finding percentages using a normal distribution table or calculator. Additionally, if you are using a specific statistical software or calculator, you can refer to their documentation or user guide for instructions on how to calculate percentages with given values.