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:
\(\mathbf{p = 0.15}\) --- the probability that a patient dies from a certain disease
\(\mathbf{n = 150}\) --- 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:
\(\mathbf{Pr = 1 - p}\)
Substitute 0.15 for p
\(\mathbf{Pr = 1 - 0.15}\)
\(\mathbf{Pr = 0.85}\)
So, the mean that a selected patient does not die is:
\(\mathbf{Mean = n \times Pr}\)
This gives
\(\mathbf{Mean = 150 \times 0.85}\)
\(\mathbf{Mean = 127.50}\)
Hence, the mean that such patients do not die is 127.50
(b) The variance
The variance is calculated using:
\(\mathbf{Variance = n \times Pr \times (1 - Pr)}\)
So, we have:
\(\mathbf{Variance = 150 \times 0.85 \times (1 - 0.85)}\)
\(\mathbf{Variance = 150 \times 0.85 \times 0.15}\)
\(\mathbf{Variance = 19.13}\)
Hence, the variance that such patients do not die is 19.13
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