Listed below are the ACT scores of 40 randomly selected students at a major university. (Use technology if you wish, Excel) 18 1
6 26 19 22 25 26 19 13 14 25 14 15 19 25 24 24 21 19 20 24 23 17 21 20 25 18 23 19 18 15 22 1912 18 13 13 21 19 17 W = 26-12= 1.75=2 (a) Construct a frequency table for the data, using 8 classes. Show W. Using the table, answer the following questions: (b) If the university wants to accept the top 90% of the applicants, what should the minimum score be? (c) If the university sets the minimum ACT score at 20, what percent of the applicants will be accepted?
1 answer:
Answer:
A) See the picture
B) 14
C) 45%
Step-by-step explanation:
A) To create a histogram like the one on the picture you can use an online tool like socscistatistics where the number of classes is customizable
B) Because the question B and C have to be responded using a frequency table with 8 classes the answer is 14; the method of using cumulative frequency tables should only be considered as a way of estimation, that is because you obtain values that depend on your choice of class intervals. The way to get a better answer would be to use all the scores in the distribution
Pc1 = 100*(4/40) = 10
Pc2 = 100*(4/40) = 10
Pc3 = 100*(3/40) = 7.5
Pc4 = 100*(11/40) = 27.5
Pc5 = 100*(5/40) = 12.5
Pc6 = 100*(4/40) = 10
Pc7 = 100*(7/40) = 17.5
Pc8 = 100*(2/40) = 5
Pc8 + Pc7 + Pc6 + Pc5 + Pc4 + Pc3 + Pc2 = 90%
Therefore, From class 8 to class 2 is the top 90% of the applicants and the minimum score is 14.
C) Scores equal to or greater than 20 are from class 8 to class 5
Pc8 + Pc7 + Pc6 + Pc5 = 45%
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Answer:
Part A: f(x) = 4·x² - 7·x-15 = (x - 3)·(4·x + 5)
Part B: The x-intercepts are x = 3 and -1.25 #
Part C: As x approaches ∞, y approaches ∞, as x approaches -∞, y approaches ∞
Part D: The graph is a u-shaped quadratic equation graph passing though the x-intercept points -1.25 and 3 on the x-axis and the y-intercept point -15 on the y-axis. Both sides of the symmetrical graph curve extending to infinity
Step-by-step explanation:
The function 4·x² - 7·x-15
To factorize the expression, we have at the 0 factors;
Where;
a = 4, b = -7, c -15, substituting gives;
Which gives;
(x - 3)·(x + 1.25) = (x - 3)·(4·x + 5)
f(x) = 4·x² - 7·x-15 = (x - 3)·(4·x + 5)
Part B: The x-intercepts are the point where y = 0, which are x = 3 and -1.25 as shown above
Part C: As x approaches ∞, y approaches ∞, as x approaches -∞, y approaches ∞
Part D: With the the nature of the function as y approaches ∞ and -∞ the graph is a u-shaped graph of a quadratic equation passing though the points -1.25 and 3 on the x-axis and the point -15 on the y-axis.