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11111nata11111 [884]
3 years ago
15

The average number of tunnel construction projects that take place at any one time in a certain state is 3. Find the probability

of exactly five tunnel construction projects taking place in this state.
Mathematics
1 answer:
slega [8]3 years ago
6 0

Answer: 0.1008188

Step-by-step explanation:

The question will usng the poisson distribution formula:

Given :

Mean(λ) number of occurrence in a given interval = 3

P(X=x) = Probability of exactly x occurrence in a given interval

Number of desired occurence(x) = 5

P(X=x) = [(λ^x) * (e^-λ)] / x!

Where ; e = base of natural logarithm = 2.7182818

P(X=5) = [(3^5) * (e^-3)] / 5!

P(X=5) = [(243) * (0.0497870)] / 120

P(X=5) = [12.098257] / 120

P(X=5) = 0.1008188

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A survey is planned to estimate the proportion of voters who support a proposed gun control law. The estimate should be within a
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Complete Question

A survey is planned to estimate the proportion of voters who support a proposed gun control law. The estimate should be within a margin of error of ±5% with 90% confidence, and we do not have any prior knowledge about the proportion who might support the law. How many people need to be included in the sample?

Round your answer up to the nearest integer.

sample size = _____

Answer:

The sample size is n = 271    

Step-by-step explanation:

From the question we are told that  

   The margin of error is  E = 5% = 0.05

Generally given that there was no prior knowledge about the proportion of who might support the law, we will assume the sample proportion to be  

     \^ p =  0.5

From the question we are told the confidence level is  90% , hence the level of significance is    

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=>   \alpha = 0.05

Generally from the normal distribution table the critical value  of  \frac{\alpha }{2} is  

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Generally the sample size is mathematically represented as  

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=>   n = 271    

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2 years ago
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