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Arte-miy333 [17]
3 years ago
12

The largest z-score available in most tables is 2.99, which corresponds to a probability of 99.86%. A fair coin is

Mathematics
1 answer:
lana66690 [7]3 years ago
5 0

Answer:

The number of heads observed is 121.14 heads

Step-by-step explanation:

The formula for the z-score of a proportion is given as follows;

z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{pq}{n}}}

Where:

{\hat{p} = Sample proportion

p = Population success proportion = 0.5

q = 1 - p = 1 - 0.5 = 0.5

n = Number in of observation = 200

z = 2.99

Hence, we have;

z=\dfrac{\hat{p}-0.5}{\sqrt{\dfrac{0.5 \times 0.5}{200}}} = 2.99

Therefore;

{\hat{p}-0.5}{} = 2.99 \times \sqrt{\dfrac{0.5 \times 0.5}{200}} = 2.99 \times\dfrac{\sqrt{2} }{40}

{\hat{p} = 0.6057

Whereby \ \hat p = \dfrac{Number \ of \ heads}{Number \ of \ observation} =  \dfrac{Number \ of \ heads}{200} = 0.6057

∴ The number of heads observed = 200 × 0.6057 = 121.14 heads.

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