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1 answer:
Step-by-step explanation:
1. Not all rational numbers are whole numbers. Whole numbers can be rational numbers, if expressed in fraction form. For example, 1 can be expressed as . A set of rational numbers consists of a set of numbers written as a quotient of two integers, a and b, in the form
, where b ≠ 0. The reason why b ≠ 0 because division by zero is an undefined mathematical operation.
2. Irrational numbers differ from rational numbers in terms of its representation: while the rational numbers can be expressed as a ratio or in fraction form, irrational numbers <em>cannot</em> be expressed in fraction form.
Irrational numbers are a set of numbers for which its decimal representations is neither <em><u>terminating</u></em>, nor <em><u>repeating</u></em>. A couple examples of irrational numbers are: π and , as their decimal representations do not come to an end and doesn't have a block of repeating digits.
3. All real numbers are rational numbers. <u>Real numbers</u> comprise of natural numbers, whole numbers, integers, rational numbers, and irrational numbers.
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Answer:
P(X ≥ 125) = 0.9812
Step-by-step explanation:
To solve this question, we need to understand the Poisson distribution and the normal distribution.
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, which is the same as the variance.
Normal distribution:
When the distribution is normal, we use 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.
The Poisson can be approximated to the normal, with
Let μ = 2.5 every minute
This is the mean of the Poisson, so , in which n is the number of minutes.
P(X ≥ 125) over an hour
An hour has 60 minutes, so
Using continuity correction, this is , which is 1 subtracted by the pvalue of Z when X = 124.5. So
has a pvalue of 0.0188
1 - 0.0188 = 0.9812
So
P(X ≥ 125) = 0.9812