The mean value of a dataset is the expected value or average value of the dataset.
- The mean that such patients do not die is 127.50
- The variance that such patients do not die is 19.13
The given parameters are:
[tex]\mathbf{p = 0.15}[/tex] --- the probability that a patient dies from a certain disease
[tex]\mathbf{n = 150}[/tex] --- the sample size
(a) The mean value of patient that do not die
First, we calculate the probability that a patient does not die.
Using the complement rule, the probability is:
[tex]\mathbf{Pr = 1 - p}[/tex]
Substitute 0.15 for p
[tex]\mathbf{Pr = 1 - 0.15}[/tex]
[tex]\mathbf{Pr = 0.85}[/tex]
So, the mean that a selected patient does not die is:
[tex]\mathbf{Mean = n \times Pr}[/tex]
This gives
[tex]\mathbf{Mean = 150 \times 0.85}[/tex]
[tex]\mathbf{Mean = 127.50}[/tex]
Hence, the mean that such patients do not die is 127.50
(b) The variance
The variance is calculated using:
[tex]\mathbf{Variance = n \times Pr \times (1 - Pr)}[/tex]
So, we have:
[tex]\mathbf{Variance = 150 \times 0.85 \times (1 - 0.85)}[/tex]
[tex]\mathbf{Variance = 150 \times 0.85 \times 0.15}[/tex]
[tex]\mathbf{Variance = 19.13}[/tex]
Hence, the variance that such patients do not die is 19.13
Read more about mean and variance at:
https://brainly.com/question/1906955
