1) To find the confidence interval
the sample mean x = 38 σ = 9; n = 85;
The confidence level is 95% (CL = 0.95) <span>CL = 0.95
so α = 1 – CL = 0.05
</span><span>α/2 = 0.025 </span>Z(α/2) = z0.025
The area to the right of Z0.025 is 0.025 and the area to the left of Z0.025 is 1 – 0.025 = 0.975
Z(α/2) = z0.025 = 1.645 This can be found using a computer, or using a probability table for the standard normal distribution.
<span>EBM = (1.645)*(9)/(85^0.5)=1.6058</span> x - EBM = 38 – 1.6058 = 36.3941 <span> x + EBM = 38 + 1.6058 = 39.6058
</span>The 95% confidence interval is (36.3941, 39.6058).
The answer is the letter D
<span>The value of 40.2 is <span>within the 95% confidence interval for the mean of the sample
</span></span>2) To find the confidence interval <span>
<span>the sample mean x = </span>76 σ = 20; n = 102; </span><span>
The confidence level is 95% (CL = 0.95) CL = 0.95
so α = 1 – CL = 0.05
α/2 = 0.025 Z(α/2) = z0.025
The area to the right of Z0.025 is 0.025 and the area to the
left of Z0.025 is 1 – 0.025 = 0.975
Z(α/2) = z0.025 = 1.645 This can be found using a computer,
or using a probability table for the standard normal distribution.
EBM = (1.645)*(20)/(102^0.5)=3.2575 x - EBM = 76 – 3.2575 = 72.7424 </span> x +
EBM = 76 + 3.2575 = 79.2575 <span>
The 95% confidence interval is (</span>72.7424 ,79.2575).<span>
The answer is the letter </span>A
and the letter D<span>
The value of 71.8 and 79.8 <span> are </span> outside<span>
the 95% confidence interval for the mean of the sample</span></span>
Answer:
1
Step-by-step explanation:
3x-6>-3 =
3x>3 =
x=1
Answer:
The power of the polynomial determines the number of zeroes it has in this case power is 4 so 4 zeroes. Whereas in 5^3+4 it has 3 zeroes as its power is 3. U can find the zero by trial and error method.
Hope this helps.
Step-by-step explanation:
Answer:
Step-by-step explanation:
The equation of a straight line can be represented in the slope intercept form as
y = mx + c
Where
m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)
The equation of the given line is
y = 7x - 5
Comparing with the slope intercept form, slope = 7
If two lines are parallel, it means that they have the same slope. Therefore, the slope of the line passing through (2, 1) is 7
To determine the intercept, we would substitute m = 7, x = 2 and
y = 1 into y = mx + c. It becomes
1 = 7 × 2 + c = 14 + c
c = 1 - 14
c = - 13
The equation becomes
y = 7x - 13
If the two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line.
Therefore, the slope of the line passing through (2, 1) is - 1/7
To determine the intercept, we would substitute m = - 1/7, x = 2 and
y = 1 into y = mx + c. It becomes
1 = - 1/7 × 2 + c = - 2/7 + c
c = 1 + 2/7
c = 9/7
The equation becomes
y = - x/7 + 9/7
Answer:
0
Step-by-step explanation:
All of the terms have positive signs, so there are no sign changes. Zero sign changes means there are zero positive real roots.
