Mark is planning to run in a 10-km race he will have to run 1 4/5 km uphill, 2 7/10 km downhill, and the rest of the race on lev
1 answer:
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Answer:
a) There is a 9% probability that a drought lasts exactly 3 intervals.
There is an 85.5% probability that a drought lasts at most 3 intervals.
b)There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation
Step-by-step explanation:
The geometric distribution is the number of failures expected before you get a success in a series of Bernoulli trials.
It has the following probability density formula:
In which p is the probability of a success.
The mean of the geometric distribution is given by the following formula:
The standard deviation of the geometric distribution is given by the following formula:
In this problem, we have that:
So
(a) What is the probability that a drought lasts exactly 3 intervals?
This is
There is a 9% probability that a drought lasts exactly 3 intervals.
At most 3 intervals?
This is
Previously in this exercise, we found that
So
There is an 85.5% probability that a drought lasts at most 3 intervals.
(b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?
This is .
We are working with discrete data, so 3.66 is rounded up to 4.
Either a drought lasts at least four months, or it lasts at most thee. In a), we found that the probability that it lasts at most 3 months is 0.855. The sum of these probabilities is decimal 1. So:
There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation
Answer:
Number of quarters → 15
Number of dimes → 2
Step-by-step explanation:
Let the number of dimes I have = y
And number of quarters = x
Since, I have amount in my pocket = $2
Therefore, 0.10y + 0.25x = 2
100(0.10y + 0.25x) = 100×2
25x + 10y = 200
5x + 2y = 40
2y = -5x + 40
y = -2.5x + 20 ---------(1)
Total number of coins in my pocket = 17
x + y = 17
y = -x + 17 ---------(2)
By using a graphing calculator we can graph these two lines (As attached)
Solution of the given system of equations will be the point of intersection of these lines.
Solution → (2, 15)
Number of quarters → 15
Number of dimes → 2
