Traveling miles on this taxi costs
In fact, we spend 2.50 no matter what, and then we add 3.25 (i.e. the cost of a mile) multiplied by the number of miles.
This quantity has to be less than or equal to 61, so we have
Solving for , we start by subtracting 2.5 from both sides:
Then, we divide both sides by 3.25:
Answer:
a)
b)
And adding these values we got:
c) We can find the expected value given by:
And the standard deviation would be:
We can use the approximation to the normal distribution and we have at leat 95% of the data within 2 deviations from the mean. And the lower limit for this case would be:
And then we can consider a value of 18 as unusual lower for this case.
Step-by-step explanation:
Let X the random variable of interest "number cleared by arrest or exceptional", on this case we can model this variable with this distribution:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
Part a
We want this probability:
Part b
We want this probability:
We can find the individual probabilities:
And adding these values we got:
Part c
We can find the expected value given by:
And the standard deviation would be:
We can use the approximation to the normal distribution and we have at leat 95% of the data within 2 deviations from the mean. And the lower limit for this case would be:
And then we can consider a value of 18 as unusual lower for this case.