according to an article on the Guardian website, a British woman in 2003 has probability 0.27 of living at least 100 years . suppose that you randomly select 200 women who were born in 2003 . will exactly 54 of them live at least 100 years?

No. 0.27 is the mean calculated from past data. It can’t be used to make an exact prediction. Each woman has a probability of 0.27 of living beyond 100 years. For example, if 100 women are randomly selected the probability of exactly 27 of them living 100 or more years is ¹⁰⁰C₂₇0.27²⁷0.73⁷³=0.09, or about 9%.

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MrRoyal MrRoyal · Answer 2 · 2021-12-09T17:53:13+01:00

The true statement is that, exactly 54 of the 200 samples will not live at least 100 years

The given parameters are:

[tex]p = 0.27[/tex] --- probability of living at least 100 years

[tex]n = 200[/tex] ---- the sample size

Start by calculating the expected value [tex]\bar x[/tex] using:

[tex]\bar x = np[/tex]

So, we have:

[tex]\bar x = 0.27 \times 200[/tex]

[tex]\bar x = 54[/tex]

This means that, in a sample of 200, 54 are expected to live at least 100 years.

The expected value is just an estimate, and as such it does not determine the actual number of people that will live at least 100 years.

Hence, the response to the statement is No