It cost Jocelyn $5.60 to send 56 text messages. How much would it cost to send 198
2 answers:
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note that this isn't a summation problem, it just wants to find on what day will she get 10,000,000 dollars in 1 day
convert that the pennies to make it easier (100 pennies=1 dollar so that's 1,000,000,000 or a billion pennies) (note that 1,000,000,000=10^9)
each day is 3 times of the other
first day is 1, 2nd is 1*3, 3rd day is 1*3*3, 4th day is 1*3*3*3, etc
hmm, so after n days, the number of pennies is
one long way is to keep dividing by 3 to find how many times we need to do that to find n
easier way is to do this:
1,000,000,000=
take ln of both sides
use properties of logarithms
divide both sides by ln(3)
add 1 to both sides
using your calculator we get 19.863=n
so after 19.863 days
but we need a whole number of days so round up to 20
20 days
it will be on day 20 of the month
Answer:
And we can find this probability with thi difference:
And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.
So then we expect about 72.5% of the current shipment times between 1 and 5 days
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 current shipment time of a population, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability with thi difference:
And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.
So then we expect about 72.5% of the current shipment times between 1 and 5 days