Answer:
The value of the sample mean is 78.
Step-by-step explanation:
We are given that a sample of n = 4 scores is obtained from a population with a mean of 70 and a standard deviation of 8.
Also, the sample mean corresponds to a z score of 2.00.
<em>Let </em>
<em> = sample mean</em>
The z-score probability distribution for a sample mean is given by;
Z = 
~ N(0,1)
where, 
= population mean = 70
= standard deviation = 8
n = sample size = 4
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.
<u>Now, we are given that the sample mean corresponds to a z score of 2.00 for which we have to find the value of sample mean;</u>
So, <em><u>z-score</u></em> formula is given by ;
z-score = = 
2.00 =
2.00 = 
= 70 + 8 = 78
<em>Therefore, the value of the sample mean is 78.</em>
A. -8 Because there’s a negative in -4ac
Table
<span> In favor Opposed Undecided
Grade 9 5 3 9
Grade 10 8 12 9
Grade 11 15 16 10
Grade 12 12 6 11
Probability = number of positive outcomes / number of possible outcomes
Probability that a student in grade 9 is in favor of extending the school day =
number of students in 9 grade in favor / number of students in grade 9
number of students in 9 grade in favor = 5
number of students in 9 grade = 5 + 3 + 9 = 17
Probability = 5 / 17
Answer: 5 / 17
</span>
Answer:
Step-by-step explanation:
Assume that the amount needed from the 5% acid is x and that the amount needed from the 6.5% acid is y.
We are given that:
The volume of the final solution is 200 ml
This means that:
x + y = 200
This can be rewritten as:
x = 200 - y .......> equation I
We are also given that:
The concentration of the final solution is 6%
This means that:
5%x + 6.5%y = 6% (x+y)
This can be rewritten as:
0.05 x + 0.065 y = 0.06 (x+y) ............> equation II
Substitute with equation I in equation II and solve for y as follows:
0.05 x + 0.065 y = 0.06 (x+y)
0.05 (200-y) + 0.065 y = 0.06 (200-y+y)
10 - 0.05 y + 0.065 y = 12
0.015y = 12-10 = 2
y = 2/0.015
y = 133.3334 ml
Substitute with the y in equation I to get the x as follows:
x = 200 - y
x = 200 - 133.3334
x = 66.6667 ml
Based on the above calculations:
The amount required from the 5% acid = x = 66.6667 ml
The amount required from the 6.5% acid = y = 133.3334 ml
