In a community, 5 people from Koc group, 6 people from Sabanci group and 4 peopl

Question

In a community, 5 people from Koc group, 6 people from Sabanci group and 4 people from Independent group exist as representatives. One, who does not know all these representatives, creates a random committee with 3 people in total from these representatives. With respect to this a) What is the probability of being represented in the committee with one person from each group? b) What is the probability of creating the committee from the representatives of the same group? c) What is the probability of creating the committee with 2 people from any of these three groups and 1 person from another group? Based on information from MRI Network, some job applicants are required to have several interviews before a decision is made. The number of required interviews and the corresponding probabilities are: 1 (0.09): 2 (0.31): 3 (0.37): 4 (0.12), 5 (0.05), 6 (0.05) a) Does the given information describe a probability distribution? Explain. b) Assuming that a probability distribution is described, find its mean and standard deviation? c) Use the range rule of thumb to identify the range of values for usual numbers of interviews d) Is it unusual to have a decision after just one interview? Explain. a) A simple random sample of a credit rating scores is listed below. As of this writing, the mean credit rating score was reported to be 678. Based on these results, is a credit rating score of 500 unusual? Why or why not? b) Construct a box-plot and include the values of the 5-number summary. The National Highway Traffic Safety Administration conducted crash tests of child booster seats for cars. Listed below are results from those tests, with the measurements given in hic (standard head injury condition units). Find the a) mean b) median c) mode, and d) midrange for the given data. According to the safety requirement, the hic measurement should be less than 1000 hic. Do the results suggest that all of the child booster seats meet the specified requirement? 5) a) Identify the class width, class midpoints and class boundaries for the given frequency distributions b) Construct one table that includes relative frequencies based on frequency distributions for non- filtered and filtered cigarettes, and then compare the amounts of tar in both types of cigarettes. Do the cigarette filters appear to be effective? c) Construct the cumulative frequency distributions that correspond to the frequency distributions in the question indicated.

Explanation / Answer

We have given that there are 5 people representative from Koc group,
6 people representative from Sabanci group, and 4 people from independent group,

Now here we want to find probability of a group of 3 people representatives in following ways;

a) Probability of being represented in the commitee with one person from each group:

Let N = total number of representatives from all groups = 5 + 6 + 4 = 15

Now one person from each group can be formed by following ways;

5C1 from Koc AND 6C1 from Sabanci AND 4C1 from independent

So probability of being represented in the commitee with one person from each group = (5C1 * 6C1 * 4C1) / 15C3

= 120 / 455 = 0.2637

b) Probability of creating the commitee from the representative of same groups

So we want to find the number of ways to create the commitee from same groups,

i.e. choose 3 people from Koc group OR choose 3 people from Sabanci group OR choose 3 people from independent group

i.e. 5C3 OR 6C3 OR 4C3, hence the probability is given by,

(5C3 + 6C3 + 4C3) / 15C3 = (10 + 20 + 4) / 455 = 34 / 455 = 0.0747

c) Probability of creating a commitee of 2 from any of the 3 groups and and 1 person from another group

2 people from any of the three group and 1 from another group

So we need to choose 2 people out of 12 peoples instead of all the 15 people, because 1 person from any other group must be selected, so to avoid repetitive selection we can consider following way,

i.e. 12C2 AND 3C1

so required probability is given by, (12C2 * 3C1) / 15C3 = (66 * 3) / 455 = 198/455 = 0.4352

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---