Answer:
The 90% confidence interval for the average monthly residential water usage for all households in this city is between 4401.3 gallons and 4598.7 gallons.
Step-by-step explanation:
We have that to find our
level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of
.
So it is z with a pvalue of
, so 
Now, find the margin of error M as such

In which
is the standard deviation of the population and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 4500 - 98.7 = 4401.3 gallons
The upper end of the interval is the sample mean added to M. So it is 4500 + 98.7 = 4598.7 gallons
The 90% confidence interval for the average monthly residential water usage for all households in this city is between 4401.3 gallons and 4598.7 gallons.
Answer:
a: no the sample size is too small
b: Yes, the distribution is normal with a mean of 40 and standard deviation of 12
Step-by-step explanation:
a: If n < 30, we need to know that the sample is normally distributed or else we can't determine anything. When sample sized get very large, they usually resemble normally distributed data sets so we can still make conjectures even if the data isn't officially normally distributed
b: The question tells us that the sample is normally distributed, so even though n < 30, we can still make conjectures about the population
Answer:
I used Desmos to graph your requirements, and i took a screenshot of the graph. Credit to Desmos for the great graphing system.
Step-by-step explanation:
The dog eats 6 cupcakes in 22 days.
<em>(don't know why a dog would be eating cupcakes in the first place, but sometimes math questions don't make the most sense)</em>
Answer:
The numbers are 12 and 3.
Step-by-step explanation:
We can solve this problem by working with the information we have and setting up some equations.
We know that one number is four times as large as another. So, let the smaller number be represented by the variable x and the bigger number be represented by 4x, since it is four times as large.
Now, we know that if the numbers are added together, then the result is six less than seven times the smaller number. This can also be represented by the equation 4x + x = 7x - 6.
Let's solve that equation like so:

So, the smaller number must be 3 (remember that x represented the smaller number). To find the bigger number, all we need to do is multiply 3 by 4, which gives us 12. Therefore, the numbers are 12 and 3.