You invest $5000 into an account earning 4% interest compounded quarterly. Write an
1 answer:
Answer:
A (in $USD) = 5,000(1 + .04/4)^4(8)
A = 5000(1 + 0.01)^32
A = 5000(1.01)^32
A = 5000(1.37494068)
A ≈ 6874.7034
<u>A = $6875 or $6875.7 (depending on rounding requirement)</u>
Step-by-step explanation:
Compound Interest Formula
A = P(1+ r/n)^n(t)
- A is the amount in the account after t years
- P is the principal (original amount invested)
- r is the annual rate, expressed as a decimal
- n the number of times the interest is calculated a year*
- t is the number of years
*If the interest is compounded monthly n = 12, if quarterly n = 4, if daily n = 365.
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Answer:
19.49% probability that no more than 16 of them are strikes
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this problem, we have that:
So
What is the probability that no more than 16 of them are strikes?
Using continuity correction, this is , which is the pvalue of Z when X = 16.5. So
has a pvalue of 0.1949
19.49% probability that no more than 16 of them are strikes