Evaluate the following: 3 Squared ÷ (2 + 1). 2 3 4 5
2 answers:
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Answer:
a) Let X the random variable of interest, on this case we know that:
This random variable represent that two people have the same birthday in just one classroom
b) We can find first the probability that one or more pairs of people share a birthday in ONE class. And we can do this:
And we can find the individual probability:
And then:
And since we want the probability in the 3 classes we can assume independence and we got:
So then the probability that one or more pairs of people share a birthday in your three classes is approximately 0.9992
Step-by-step explanation:
Previous concepts
A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
Solution to the problem
Part a
Let X the random variable of interest, on this case we know that:
This random variable represent that two people have the same birthday in just one classroom
Part b
We can find first the probability that one or more pairs of people share a birthday in ONE class. And we can do this:
And we can find the individual probability:
And then:
And since we want the probability in the 3 classes we can assume independence and we got:
So then the probability that one or more pairs of people share a birthday in your three classes is approximately 0.9992
Answer:
The 99% confidence interval would be given (11.448;14.152).
Step-by-step explanation:
1) Important concepts and notation
A confidence interval for a mean "gives us a range of plausible values for the population mean. If a confidence interval does not include a particular value, we can say that it is not likely that the particular value is the true population mean"
represent the sample deviation
represent the sample mean
n =1003 is the sample size selected
Confidence =99% or 0.99
represent the significance level.
2) Solution to the problem
The confidence interval for the mean would be given by this formula
We can use a z quantile instead of t since the sample size is large enough.
For the 99% confidence interval the value of and
, with that value we can find the quantile required for the interval in the normal standard distribution.
And replacing into the confidence interval formula we got:
And the 99% confidence interval would be given (11.448;14.152).
We are confident that about 11 to 14 are the number of books that the people had read on the last year on average, at 1% of significance.