Find the greatest number which divides 6168, 2447 and 3118 leaving the same remainder in each case.

1 answer:

5 0

let the greatest number be a and remainder be x. And let the whole number result of the division be b, c and d. So we have

ab + x = 2447............(1)

ac + x = 3118...............(2)

ad + x = 6168.............(3)

Subtracting (2) - (1) gives:-

ac - ab = 671

a(c - b) =671

Now 671 = 61 * 11 so 61 could be the value of a

Checking:- 2447 / 61 = 40 remainder 7 , 3118 / 61 = 51 remainder 7

and 6168 / 61 = 101 remainder 7

Answer 61

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And we can find this probability using the complement rule:

$P(z>-2)=1-P(z$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(z>-2)=1-P(z$

Step-by-step explanation:

Previous concepts

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(440,20)$