Since sample size is > 40, we use the z-score
in calculating for the confidence interval.
The formula is given as:
Confidence Interval = X ± z * σ / sqrt (n)
Where,
X = mean = $50,340
z = z-score which is taken from standard distribution
tables at 90% confidence interval = 1.645
σ
= standard deviation = $10,780
n = sample size = 45
Substituting to the equation:
Confidence Interval = 50,340 ± 1.645 * 10,780 / sqrt (45)
Confidence Interval = 50,340 ± 1,607
Confidence Interval = $48,733 to $51,947
<span>Therefore the salary range of the personnel is $48,733 to $51,947.</span>
-9T means -9 x T
So if T is equivalent to 4,
you should do:
-9 x 4 = -36
J= -36
No, they are not equivalent because if you distribute the -0.5 in the expression -0.5(3x+5) you will get -1.5x-2.5 which is not the same as -1.5+2.5
Answer:
57.93% probability that a trip will take at least 35 minutes.
Step-by-step explanation:
Problems of normally distributed samples are 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 problem, we have that:
What is the probability that a trip will take at least 35 minutes
This probability is 1 subtracted by the pvalue of Z when X = 35. So
has a pvalue of 0.4207
1 - 0.4207 = 0.5793
57.93% probability that a trip will take at least 35 minutes.
The answer to this depends on the angle at which they intersect. If it intersects<span> the cylinder perpendicular to the axis then a circle is formed. </span><span>If the plane intersects the cylinder at an angle, it will form an ellipse. This will be true until the plan is parallel with the axis of the cylinder. At that point, the surface will become a rectangle.</span>
