Roxanne has $20 and she wants to buy some shirts. She picks one shirt that costs $10.99 and two shirts that cost $4.99 each.
2 answers:
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Answer:
1.02% probability of spending 0 dollars on coffee over the course of a five day week
7.68% probability of spending 3 dollars on coffee over the course of a five day week
23.04% probability of spending 6 dollars on coffee over the course of a five day week
34.56% probability of spending 9 dollars on coffee over the course of a five day week
25.92% probability of spending 12 dollars on coffee over the course of a five day week
7.78% probability of spending 12 dollars on coffee over the course of a five day week
Step-by-step explanation:
For each day, there are only two possible outcomes. Either the subway is on time, or it is not. Each day, the probability of the train being on time is independent from other days. So we use the binomial probability distribution to solve this problem.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
In this problem we have that:
The probability that the subway is delayed is 40%. 100-40 = 60% of the train being on time, so
The week has 5 days, so
She spends 3 dollars on coffee each day the train is on time.
Probabability that she spends 0 dollars on coffee:
This is the probability of the train being late all 5 days, so it is P(X = 0).
1.02% probability of spending 0 dollars on coffee over the course of a five day week
Probabability that she spends 3 dollars on coffee:
This is the probability of the train being late for 4 days and on time for 1, so it is P(X = 1).
7.68% probability of spending 3 dollars on coffee over the course of a five day week
Probabability that she spends 6 dollars on coffee:
This is the probability of the train being late for 3 days and on time for 2, so it is P(X = 2).
23.04% probability of spending 6 dollars on coffee over the course of a five day week
Probabability that she spends 9 dollars on coffee:
This is the probability of the train being late for 2 days and on time for 3, so it is P(X = 3).
34.56% probability of spending 9 dollars on coffee over the course of a five day week
Probabability that she spends 12 dollars on coffee:
This is the probability of the train being late for 1 day and on time for 4, so it is P(X = 4).
25.92% probability of spending 12 dollars on coffee over the course of a five day week
Probabability that she spends 15 dollars on coffee:
Probability that the subway is on time all days of the week, so .
7.78% probability of spending 12 dollars on coffee over the course of a five day week
Answer:
see the explanation
Step-by-step explanation:
we know that
step 1
The compound interest formula is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
substitute in the formula above
Applying property of exponents
step 2
The formula to calculate continuously compounded interest is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
e is the mathematical constant number
we have
substitute in the formula above
Applying property of exponents
step 3
Compare the final amount
therefore
Find the difference
----> Additional amount of money you would have in your pocket if you had used a continuously compounded account with the same interest rate and the same principal.