Answer:
The minimum score required for admission is 21.9.
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:
A university plans to admit students whose scores are in the top 40%. What is the minimum score required for admission?
Top 40%, so at least 100-40 = 60th percentile. The 60th percentile is the value of X when Z has a pvalue of 0.6. So it is X when Z = 0.255. So
The minimum score required for admission is 21.9.
The coordinates of X are (5, 11).
Solution:
Given points of the line segment are P(2, 2) and T(7, 17)
Let X be the point that partitions the directed line segment PT in the ratio 3 : 2
Using section formula, we can find the coordinate of the point that partitions the line segment.
Section formula:
Here, and m = 3, n =2
Substitute these in the section formula,
X(x, y) = (5, 11)
The coordinates of X are (5, 11).
For this case we have that by definition, the area of a triangle is given by:
Where:
h: It's the height of the triangle
b: It is the base of the triangle.
They tell us that the height of the triangle is 3 units more than the base. That means that if the base is "b" then the height is "b + 3". So, the area is:
ANswer:
Option C
The race with 5 runners can be completed in 120 ways. The number of ways in which B finish first and D finish second is 6 ways. The probability that B finishes first and D finishes second is 0.01667
A permutation is referred to as the number of ways in which linear elements can be arranged in an orderly manner. It is usually expressed by the formula:
The number of different ways in which a race with 5 runners can be completed can be estimated by using permutation.
= 120 ways
If we fix B at first and D at second, then, the number of ways in which B and D can finish first and second respectively is:
= 6 ways
We know that the total number of ways A, B, C, D, and E can finish the race = 5!
The total number of ways B and D finish first and second is = 2!
∴
The probability that B and D finish 1st and 2nd respectively can be computed as:
Learn more about permutation here: