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Suppose it is believed that the probability a patient will die from a certain disease following treatment is 0.15. In a group of 150 such patients, the number who do not die would have mean and variance respectively given by (to two decimal places):

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what doe you mean and what is the question?


MrRoyal

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

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