Question Two is D. $14.80
Answer:
The score that separates the lower 5% of the class from the rest of the class is 55.6.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean 
and standard deviation 
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
Find the score that separates the lower 5% of the class from the rest of the class.
This score is the 5th percentile, which is X when Z has a pvalue of 0.05. So it is X when Z = -1.645.
The score that separates the lower 5% of the class from the rest of the class is 55.6.
Answer:
C
Step-by-step explanation:
Firstly, we set up the null and alternative hypothesis as follows;
The null hypothesis is;
H0: μ ≥ 12
The alternative hypothesis is;
Ha : μ < 12
Next step is to calculate the test statistic z
Mathematically;
z = (x - μ )/ σ /√n
= (11.58 - 12) /1.93/√(80
Test statistic z = -1.92
Now we proceed to find the probability value that is equal to the value of the test statistic. We can find this by using the standard normal table or NORMSTD function on excel
P(z < -1.92) = 0.0274
P-value = 0.0274
alpha = 0.05
From the above, we can see that
P-value < alpha
And because of this, we are going to reject the null hypothesis and therefore accept the alternative.
We then conclude that there is sufficient evidence to conclude that "The average battery life (between charges) of this model of tablet is at least 12 hours."
Answer:
By AA similarity
Step-by-step explanation:
We have been given that ABCD is a parallelogram
So, by the property of parallelogram AB ||CD and FD is cutting the line BC
Hence, FD is transverse line. In transverse line alternate angles are equal.
Therefore, ∠AFD=∠EDC (alternate interior angles)
And ∠FAD=∠ECD (opposite angles in parallelogram)
Therefore, by AA similarity △ADF∼△CDE
Answer:
One
Explanation:
3
y
=
18
x
+
21
XXX
⇔
y
=
6
x
+
7
5
y
+
55
=
30
x
XXX
⇔
y
=
6
x
−
11
both equations are linear and they are not co-linear
therefore there is exactly 1 solutio
