Is the sum of two rational numbers always rational
1 answer:
Answer:
in short, Yes they are always rational.
here's why...
E.g. suppose and
are fractions, that means that a,b,c,d are all integers, and b and d are not zero. finding the sum the numerator, and denominator would also have to be integers. the denominator of the sum can't be zero since the denominators of the fractions were not zero, and would give
and since they are bound by addition (sum means addition) they must also be rational since eit would equal a bigger integer than initially had
Step-by-step explanation:
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Answer:
See explanation below.
Step-by-step explanation:
Assuming this problem: "According to New Jersey Transit, the 8:00 A.M. weekday train from Princeton to New York City has a 90% chance of arriving on time on a randomly selected day. Suppose this claim is true. Choose 6 days at random. Let W = the number of days on which the train arrives late. "
For this case we can check if the binomial model can be used checking conditions:
1) We satisfy that we have independent trials and is assumed for this case
2) We have a fixed value for the trials n =6 and for the probability p = 0.9 on each trial
3) We have bernoulli experiments on each trial since we have success or failure for each case.
So then since all the conditions are satisfied we can assume that the binomial model can be used here.
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".
Let W the random variable of interest "the number of days on which the train arrives late", on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
We can find all the possible probabilities for all the possible values of X like this:
Answer:
For this case we want to find this probability:
And we can use the z score formula to see how many deviation we are within the mean and we got:
And for this case we know that within 3 deviation from the mean we have 99.7% of the values and that's the answer for this case.
Step-by-step explanation:
Previous concepts
The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".
Let X the random variable who represent the number of phone calls answered.
From the problem we have the mean and the standard deviation for the random variable X.
So we can assume
On this case in order to check if the random variable X follows a normal distribution we can use the empirical rule that states the following:
• The probability of obtain values within one deviation from the mean is 0.68
• The probability of obtain values within two deviation's from the mean is 0.95
• The probability of obtain values within three deviation's from the mean is 0.997
Solution to the problem
For this case we want to find this probability:
And we can use the z score formula to see how many deviation we are within the mean and we got:
And for this case we know that within 3 deviation from the mean we have 99.7% of the values and that's the answer for this case.