Suppose that prior to conducting a coin-flipping experiment, we suspect that the coin is fair. How many times would we have to f
1 answer:
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<h3>Answer: Choice B</h3>
The set notation includes all values from -5 to 0, but the domain only includes the integer values
eg: something like -1.2 is in the second set, but it is not in the set {-5,-4,-3,-2,-1}
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Further explanation:
Let's go through the answer choices one by one
- A. This is false because 0 does not come before -5, but instead -5 is listed first. The order -5,-4,-3,-2,-1,0 is correct meaning that
is the correct order as well.
- B. This is true. A value like x = -1.2 is in the set
since -1.2 is between -5 and 0; but -1.2 is not in the set {-5, -4, -3, -2, -1, 0}. So the distinction is that we're either considering integers only or all real numbers in this interval. To ensure that we only look at integers, the student would have to write
. The portion
means "x is in the set of integers". The Z refers to the German word Zahlen, which translates to "numbers".
- C. This is false. The student used the correct inequality signs to indicate x is -5 or larger and also 0 or smaller; basically x is between -5 and 0 inclusive of both endpoints. The "or equal to" portions indicate we are keeping the endpoints and not excluding them.
- D. This is false. Writing
would not make any sense. This is because that compound inequality breaks down into
. Try to think of a number that is both smaller than -5 AND also larger than 0. It can't be done. No such number exists.
Answer:
The 95% confidence interval for the average monthly electricity consumed units is between 47.07 and 733.87
Step-by-step explanation:
We have the standard deviation for the sample. So we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 45 - 1 = 44
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 44 degrees of freedom(y-axis) and a confidence level of . So we have T = 2.0141
The margin of error is:
M = T*s = 2.0141*170.5 = 343.4
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 390.47 - 343.40 = 47.07 units per month
The upper end of the interval is the sample mean added to M. So it is 390.47 + 343.40 = 733.87 units per month
The 95% confidence interval for the average monthly electricity consumed units is between 47.07 and 733.87