18. Please answer questions 18-19 using the following information:
Class Scores Frequency - f
Lower limit < score < upper limit
20-30 6
30-40 10
40-50 12
50-60 8
60-70 4
What is the probability that a selected observation is between 40 and 50?
(Points: 5)
0.25
0.30
0.40
0.65
19. What is the probability that a selected observation is greater than 39, but less than 60? (Points: 5)
0.20
0.40
0.30
0.50
To answer these questions, we can use the concept of probability. Probability is the measure of the likelihood that an event will occur.
To find the probability of a selected observation falling within a specific range (i.e., between two values), we need to determine the total number of observations within that range, and then divide it by the total number of observations in the entire dataset.
Let's calculate the probabilities for questions 18 and 19:
Question 18: What is the probability that a selected observation is between 40 and 50?
First, let's find the total number of observations between 40 and 50. From the given information, we can see that the frequency (f) for the class scores between 40 and 50 is 12.
Next, let's calculate the total number of observations in the entire dataset. Summing up the frequencies for all class scores, we get: 6 + 10 + 12 + 8 + 4 = 40.
Now, we can calculate the probability by dividing the number of observations between 40 and 50 (12) by the total number of observations (40):
Probability = 12 / 40 = 0.30
So, the probability that a selected observation is between 40 and 50 is 0.30.
Question 19: What is the probability that a selected observation is greater than 39 but less than 60?
To find the answer, we need to calculate the total number of observations between 39 and 60. From the given information, we can add the frequencies for the class scores between 40-50 and 50-60: 12 + 8 = 20.
Again, we calculate the total number of observations in the entire dataset (40).
Now, we divide the number of observations between 39 and 60 (20) by the total number of observations (40):
Probability = 20 / 40 = 0.50
So, the probability that a selected observation is greater than 39 but less than 60 is 0.50.
The answers to questions 18 and 19 are:
Question 18: The probability that a selected observation is between 40 and 50 is 0.30.
Question 19: The probability that a selected observation is greater than 39, but less than 60 is 0.50.