The score obtained by 100 applicants on an aptitude tests for selection into a program are shown in the frequency table.
Score Frequency Cumulative Freq
0-9 8 8
10-19 13 8+13=21
20-29 17 21+17=38
30-39 20 38+20=58
40-49 19 58+19=77
50-59 14 77+14=91
60-69 6 91+6=97
70-79 3 67+3=100
(a)Draw a cumulative frequency curve using 2cm to represent each class interval and 2cm to represent 10 applicants.
(b)Using your curve,answer the following:
(i)A score of 45 was considered as acceptable for the program.Estimate the number of applicants who qualified for entry.
(ii)Assuming there were places for only 15 applicants,estimate the lowest score that would be used to select them.
(iii)Calculate the probability that an applicant chosen at random obtained a score of at least 45.
Please help me. Thank you.
Well, I am not certain what you don't understand. You are given the data points. for instance, at 59, you have the point (59,91)
do all the points that way, then plot.
To draw a cumulative frequency curve, you will need to use the given frequency table. Here's how you can create the cumulative frequency curve:
Step 1: Create a table with three columns: Score, Cumulative Frequency, and Cumulative Frequency Percentage.
Step 2: Fill in the Score column with the given score intervals: 0-9, 10-19, 20-29, 30-39, 40-49, 50-59, 60-69, 70-79.
Step 3: Fill in the Cumulative Frequency column with the cumulative frequencies given in the frequency table: 8, 21, 38, 58, 77, 91, 97, 100.
Step 4: Calculate the Cumulative Frequency Percentage by dividing each cumulative frequency by the total number of applicants (100) and multiply by 100.
Step 5: Create a graph with two axes: x-axis representing the score intervals and y-axis representing the cumulative frequency percentage.
Step 6: Plot points on the graph using the score intervals as x-coordinates and the cumulative frequency percentages as y-coordinates. Connect the points with a smooth curve.
Now, let's move on to answering the questions using the cumulative frequency curve:
(a) You will need to draw the cumulative frequency curve using the steps mentioned above.
(b) (i) To estimate the number of applicants who qualified with a score of 45, locate the score of 45 on the x-axis of the cumulative frequency curve and draw a vertical line to intersect the curve. From that intersection point, draw a horizontal line to the y-axis. Read the corresponding value on the y-axis, which represents the cumulative frequency percentage. Multiply this percentage by the total number of applicants (100) to get the estimated number of applicants who qualified.
(ii) If there were places for only 15 applicants, locate the score of 15 on the y-axis and draw a horizontal line to intersect the cumulative frequency curve. From that intersection point, draw a vertical line to intersect the x-axis. Read the corresponding value on the x-axis, which represents the lowest score used to select the 15 applicants.
(iii) To calculate the probability that an applicant chosen at random obtained a score of at least 45, subtract the cumulative frequency percentage at the score of 45 from 100%. This will give you the percentage of applicants who scored at least 45. To convert it to a probability, divide the percentage by 100.
I hope this helps! Good luck with your calculations and graphing.