A standard six-sided die is rolled 6 times. You are told that among the rolls, there was one 1, two 2's, and three 3's. How many
2 answers:
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<h3>Solution:</h3>
Answer:
1. c. Poisson
2. 0.9592 = 95.92% probability that in any one minute at least one purchase is made.
3. 0.0017 = 0.17% probability that no one makes a purchase in the next 2 minutes.
Step-by-step explanation:
We have only the mean, which means that the Poisson distribution is used to solve this question, and thus the answer to question 1 is given by option c.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given interval.
Mean of 3.2 minutes:
This means that , in which n is the number of minutes.
2. What is the probability that in any one minute at least one purchase is made?
, so
.
This probability is:
In which
So
0.9592 = 95.92% probability that in any one minute at least one purchase is made.
3. What is the probability that no one makes a purchase in the next 2 minutes?
2 minutes, so
This probability is P(X = 0). So
0.0017 = 0.17% probability that no one makes a purchase in the next 2 minutes.