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Answer:
The distribution of proportion of people who will get the flu this winter is <em>N</em> (0.065, 0.014²).
Step-by-step explanation:
Let <em>X</em> = number of people who will get flu this year.
The sample selected is of size, <em>n</em> = 309.
The number of people who will get flu in this sample is, <em>x</em> = 20.
Compute the sample proportion of people who will get flu as follows:
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 309 and <em>p</em> = 0.065.
The sample size is quite large, i.e. <em>n</em> = 309 > 30.
And the probability of success is low.
So the Normal approximation to Binomial can be used to approximate the distribution of sample proportion is:
- np ≥ 10
- n(1 - p) ≥ 10
Check whether the conditions are fulfilled or not as follows:
Hence, the conditions are fulfilled.
The sampling distribution of sample proportion is:
Compute the mean and variance as follows:
Thus, the distribution of proportion of people who will get the flu this winter is <em>N</em> (0.065, 0.014²).