Statistics and Probability Answers

Suppose data collected on rain fall in(mm) of 390 metrological stations were tabulated in frequency distribution and the following result were obtained.

frequency: 6, 25, 48, 72, 116, 60, 38,22,3

CM1=110; CM2=120, where ;CMi is class marks of ith class and assume the size of the class interval(w) are equal.

Determine:-

a. Class interval size, class boundaries and class marks(class mid point) of each class.

b. Compute the mean, median and the modal rain fall of the distribution.

The median and the mode of mesokurtic distribution is 32 and 34 respectively.The fourth central moment is 243 ,compute pearsonian coefficient of skwness and identify type skwness (assume n-1=n).

population consists of N=5 numbers 0, 3, 4, 9, and 15. Draw all possible samples of size n=3 without replacement, from the population and find the sample proportion of even numbers in the samples. Construct the sampling distribution of sample proportion?

1. What measures of position divides the distribution into 100 equal parts?

2. What is the equivalent of lower quartile in terms of percentile?

3. It tells where a specific data value falls within the data set or its relative position in comparison with other data values.

4. The second quartile is also the ____________.

5. The difference between Upper quartile and Lower quartile is called _____________.

For numbers 11-15, refer to the given table.

Distance (km) Travelled from Home to School of Students

18-20

15-17

12-14

9-11

6-8

3-5

0-2 

Frequency (f)

1

2

3

5

8

17

4

Lower boundaries

17.5

14.5

11.5

8.5

5.5

2.5

0.5 

Less Than Cumulative Frequency (< 𝑐𝑓)

40

39

37

34

29

21

4

11. What is the lower boundary in solving for the 45th percentile of the distance travelled from home to school of the students?

12. What is the 45th percentile of the distance travelled from home to school of the students?

13. What cumulative frequency should be used in solving for the 7th decile?

14. Find the value of D7.

15.What is the value of Q1?

A company produces machine components which pass through an automatic testing machine. 5% of the components entering the testing machine are defective. However, the machine is not entirely reliable. If a component is defective there is 4% probability that it will not be rejected. If a component is not defective there is 7% probability that it will be rejected.

a) What fraction of all the components are rejected?

b) What fraction of the components rejected are actually not defective?

c) What fraction of those not rejected are defective?