Respuesta :
Answer:
1/5
Step-by-step explanation:
Range as a measure of central tendency is the difference between the highest value and the lowest value in a given set of data.
Given the samples 0,1,3,4,7
Total number of samples is 5
The range is gotten by taking the difference of 2 samplesout of 5samples and this can be done in 5C2 ways.
5C2 = 5!/(5-2)!2!
= 5!/3!2!
= 5×4×3!/3!×2
= 10ways
The total outcome is therefore 10
To get the probability that the range is 4, we need to get the required outcome of getting range of 4 and this can only occur twice
The range can be gotten by taking the difference between 7 and 3, it can also be gotten by taking the difference between 4 and 0. Both differences will give us a total of 4
The expected outcome is therefore 2
the probability that the range of the sample is 4 = expected outcome/total outcome
= 2/10
= 1/5
Using the probability concept, it is found that there is a 0.2 = 20% probability that the range of the sample is 4.
- A probability is the number of desired outcomes divided by the number of total outcomes.
Desired outcomes:
- Range of 4, that is, a difference of 4 between the values, hence two possible outcomes, {0,4} and {3,7}.
Total outcomes:
- 2 values from a set of 5, with order not being important, as for example, {0,1} is the same outcome as {1,0}, then, using the combination formula:
[tex]T = C_{5,2} = \frac{5!}{3!2!} = 10[/tex]
The probability is:
[tex]p = \frac{D}{T} = \frac{2}{10} = 0.2[/tex]
0.2 = 20% probability that the range of the sample is 4.
To learn more about the probability concept, you can check https://brainly.com/question/24437717
