Lake Superior is the largest of the Great Lakes it covers a surface area of about 30,000 square miles. How can you show the esti
2 answers:
Answer:
The area would be,
Step-by-step explanation:
Since, a very large or very small number can be written as the product of whole number and exponent ( a power ) of ten,
If a number is very large then we move the decimal to left side so that we get a whole number then the number of shifting is the power of ten,
While when we shift the decimal to the right side then the exponent of 10 is negative.
Here, the given number,
30,000 square miles,
The number of shifting to the left so that we get a whole number is 4,
By the above statement,
30,000 =
Hence, the estimated area of the lake would be square miles
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Answer:
(26.32; 57.68)
See explanation below.
Step-by-step explanation:
Assuming the following question:
Pay your bills:
In a large sample of customer accounts, a utility company determined that the average number of days between when a bill was sent out and when the payment was made is 42 with a standard deviation of 8 days. Assume the data to be approximately bell-shaped.
Between what two values will approximately 95% of the numbers of days be?
Solution to the problem
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".
Let X the random variable that represent the average number of days between when a bill was sent out and when the payment of a population, and for this case we know the distribution for X is given by:
Where and
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.025 of the area on the left and 0.975 of the area on the right it's z=-1.96. On this case P(Z<-1.96)=0.025 and P(z>-1.96)=0.975
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 2.5% of data from the top 97.5% is 26.32.
For the other value since the distirbution is symmetric the other value that accumulates 0.975 of the area on the left and 0.025 on the right is z=1.96 and similarly:
And if we solve for a we got
So the answer for this case would be (26.32; 57.68)