Can you guys teach me how to do this??

Mathematics

1 answer:

Vadim26 [7]3 years ago

4 0

The usual margin of error we strive for is a 95% probability that our estimate is within the margin. Assuming a normal distribution (and that we have a big enough sample not to worry about t tests) that corresponds to between minus and plus two standard deviations of the mean (remember the 68-95-99.7 rule). So our margin of error is plus or minus two standard deviations.

Answer: ±2%

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Answer:

There is a 0.73% probability that Ben receives a total of 2 phone calls in a week.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

$e = 2.71828$ is the Euler number

$\mu$ is the mean in the given time interval.

The problem states that:

The number of phone calls that Actuary Ben receives each day has a Poisson distribution with mean 0.1 during each weekday and mean 0.2 each day during the weekend.

To find the mean during the time interval, we have to find the weighed mean of calls he receives per day.

There are 5 weekdays, with a mean of 0.1 calls per day.

The weekend is 2 days long, with a mean of 0.2 calls per day.

So:

$\mu = \frac{5(0.1) + 2(0.2)}{7} = 0.1286$