Answer:C. (77.29, 85.71)
Step-by-step explanation:
We want to determine a 95% confidence interval for the mean test score of randomly selected students.
Number of sample, n = 25
Mean, u = 81.5
Standard deviation, s = 10.2
For a confidence level of 95%, the corresponding z value is 1.96. This is determined from the normal distribution table.
We will apply the formula
Confidence interval
= mean +/- z ×standard deviation/√n
It becomes
81.5 +/- 1.96 × 10.2/√25
= 81.5 +/- 1.96 × 2.04
= 81.5 +/- 3.9984
The lower end of the confidence interval is 81.5 - 3.9984 =77.5016
The upper end of the confidence interval is 81.5 + 3.9984 =85.4984
Therefore, the correct option is
C. (77.29, 85.71)
The answer is:
Solve for y in the first equation
y=−5<span>
y=8−<span>x
</span></span>
<span>Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is <span>−5</span></span><span>y=−5</span><span><span>(−5)</span>=8−<span>x
</span></span>
Remove parentheses.<span>y=−5</span><span>−5=8−<span>x
</span></span>
Solve for x in the second equation.<span>y=−5</span>
<span>x=13</span>
The answer is <span>(13,−5<span>) Please mark as Brainliest
</span></span>
Number of boys in the gym class = 12
Number of girls in the gym class = 10
then
Ratio of boys to ratio of girls = 12:10
= 6:5
Now
Number of boys joining the gym class later = 6
So after the new boys join the number of boys in the gym class becomes = 18
The ratio of boys to girls have to remain the same
Let us assume that the number of girls that need to join the gym class = x
Then
6/5 = 18/(x + 10)
6(x + 10) = 18 * 5
6x + 60 = 90
6x = 90 - 60
6x = 30
x = 30/6
= 5
So the number of girls that need to join the gym class to keep the ratio same is 5. I hope the procedure is clear enough for you to understand.
emmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmStep-by-step explanation:
Answer:
And if we replace we got 
D. The statistics are representative because they are taken from a random sample
Step-by-step explanation:
For this case we have the following data:
9.9 8.7 10.1 9.2 9.2 9.9 10.1 9.4 9.1 9.3 10.2
The data was colledted from a random sample of people selected in 1988.
We can order the dataset on increasing way and we got:
8.7 9.1 9.2 9.2 9.3 9.4 9.9 9.9 10.1 10.1 10.2
The range is defined as
The mean is defined as:
The standard deviation can be calculated with the following formula:
And if we replace we got
The sample variance would be just the deviation squared:
And since the data comes from a random sample then is representative fo the population data in 1988. So then the best answer for this case would be:
D. The statistics are representative because they are taken from a random sample
