A child has a box full of colored building blocks. She will choose one block without looking. The odds against choosing a blue b
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Answer:
The 98% confidence interval would be given by (0.326;0.354)
Step-by-step explanation:
1) Notation and definitions
number of people who live within 20 miles of the coast in high hurricane risk counties of eight southern states
random sample taken
estimated proportion of people who live within 20 miles of the coast in high hurricane risk counties of eight southern states
true population proportion of people who live within 20 miles of the coast in high hurricane risk counties of eight southern states
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The population proportion have the following distribution
2) Confidence interval
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 98% of confidence, our significance level would be given by and
. And the critical value would be given by:
The confidence interval for the mean is given by the following formula:
If we replace the values obtained we got:
The 98% confidence interval would be given by (0.326;0.354)
Answer:
Let X the random variable of interest "number of tweets with no reaction", on this case we now that:
And the expected value is given by:
So we expect about 71 tweets with no reaction for this case.
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
Let X the random variable of interest "number of tweets with no reaction", on this case we now that:
And the expected value is given by:
So we expect about 71 tweets with no reaction for this case.