Help please, I attached the question. Is it a!? 
2 answers:
Answer:
A
Step-by-step explanation:
Recall that for a quadratic equation of the form:
The number of solutions it has can be determined using its discriminant:
Where:
- If the discriminant is positive, we have two real solutions.
- If the discriminant is negative, we have no real solutions.
- And if the discriminant is zero, we have exactly one solution.
We have the equation:
Thus, <em>a</em> = 2, <em>b</em> = 5, and <em>c</em> = -<em>k</em>.
In order for the equation to have exactly one distinct solution, the discriminant must equal zero. Hence:
Substitute:
Solve for <em>k</em>. Simplify:
Solve:
Thus, our answer is indeed A.
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Answer:
a) Standard error = 2
b) Range = (76.08, 83.92)
c) P=0.69
d) Smaller
e) Greater
Step-by-step explanation:
a) When we have a sample taken out of the population, the standard error of the mean is calculated as:
where n is te sample size (n=25) and σ is the population standard deviation (σ=10).
Then, the standard error of the classroom average score is 2.
b) The calculations for this range are the same that for the confidence interval, with the difference that we know the population mean.
The population standard deviation is know and is σ=10.
The population mean is M=80.
The sample size is N=25.
The standard error of the mean is σM=2.
The z-value for a 95% confidence interval is z=1.96.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The range that we expect the average classroom test score to fall 95% of the time is (76.08, 83.92).
c) We can calculate this by calculating the z-score of X=79.
Then, the probability of getting a average score of 79 or higher is:
The approximate probability that a classroom will have an average test score of 79 or higher is 0.69.
d) If the sample is smaller, the standard error is bigger (as the square root of the sample size is in the denominator), so the spread of the probability distribution is more. This results then in a smaller probability for any range.
e) If the population standard deviation is smaller, the standard error for the sample (the classroom) become smaller too. This means that the values are more concentrated around the mean (less spread). This results in a higher probability for every range that include the mean.