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58% of the goblins in town (our population proportion) know how to cross the bridge over...

58% of the goblins in town (our population proportion) know how to cross the bridge over River Lum. Suppose 80 goblins are randomly sampled to see whether or not they know how to cross the bridge over River Lum.

A) Find p ̂ (sample proportion), up ̂ (mean), and σ_p ̂ (standard error) for the data’s sampling distribution based on the population proportion (58%).

B) What is the probability that over 50% of the 80 goblins sampled would know how to cross the bridge over River Lum?

Math   Statistics-And-Probability   
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Answer #1

The following information has been provided about the population proportion and the sample size:

Population Proportion = 0.58
Sample Size = 80

A) Find p ̂ (sample proportion), up ̂ (mean), and σ_p ̂ (standard error) for the data’s sampling distribution based on the population proportion (58%).

B) What is the probability that over 50% of the 80 goblins sampled would know how to cross the bridge over River Lum?

We need to compute . Based on the information provided, the population men of sample proportions and the corresponding standard error are:

Now, the following is obtained using normal approximation:

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