AIMA Exam Solution 2021 GM03 BUSINESS STATISTICS

𝐀𝐢𝐦𝐚 𝐬𝐨𝐥𝐯𝐞𝐝 𝐞𝐱𝐚𝐦 𝐬𝐨𝐥𝐮𝐭𝐢𝐨𝐧𝐬 𝟐𝟎𝟐𝟏 

𝐅𝐨𝐫 𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧 𝐂𝐚𝐥𝐥 𝐚𝐭 +𝟗𝟏-𝟗𝟗𝟏𝟏𝟖𝟗𝟗𝟒𝟎𝟎 (𝐖𝐡𝐚𝐭'𝐬 𝐀𝐩𝐩 𝐀𝐯𝐚𝐢𝐥𝐚𝐛𝐥𝐞)

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Attempt all the questions. All questions are compulsory. Each question carries 4 marks. There is No Negative Marking for wrong answer/s.

Please note: There are 25 questions out of which Q.No.21-25 are based on the Case Study.

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Subject Code: GM03

Subject Name: BUSINESS STATISTICS

Component name: TERM END Assignment Start Date: 10/02/2021

Assignment End Date: 20/02/2021

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Question 1:- If P(A) = 0.3, P(B) = 0.4 and P(AUB)=0.7 then

a)   A and B are mutually exclusive                        

b)   A and B are independent                        

c)   Both (a) and (b)                        

d)   none of these                        

Question 2:- If P(A) = 0.4, P(B) = 0.3 and P(A∩B)= 0 then

a)   A and B are mutually exclusive                        

b)   A and B are independent                        

c)   Both (a) and (b)                        

d)   none of these                        

Question 3:- An unbiased coin is tossed 10 times, then probability of getting exactly 4 heads is

a)   0.377                        

b)   0.623                        

c)   0.35                        

d)   0.205                        

Question 4:- A binomial distribution with a probability of success is 0.3 is

a)   positively skewed                        

b)   negatively skewed                        

c)   symmetric                        

d)   cannot say                        

Question 5:- A binomial distribution with a probability of success is 0.7 is

a)   positively skewed                        

b)   negatively skewed                        

c)   symmetric                        

d)   cannot say                        

Question 6:- A binomial distribution with a probability of success is 0.5 is

a)   positively skewed                        

b)   negatively skewed                        

c)   symmetric                        

d)   cannot say                        

Question 7:- A Poisson distribution with a large value of mean will tend to

a)   positively skewed                        

b)   negatively skewed                        

c)   symmetric                        

d)   cannot say                        

Question 8:- If four flights land every hour on average is Poisson distribution then the average time between flight arrivals is distributed as

a)   Poisson distributed                        

b)   normal distributed                        

c)   binomial distribution                        

d)   exponential distribution                        

Question 9:- If a variable is normally distributed with a mean of 30 and standard deviation of 5 then the probability that the value of the variable is between 20 and 40 is

a)   0.626                        

b)   0.05                        

c)   0.954                        

d)   0.9                        

Question 10:- 20% of the production is done using machine A and the rest using machine B. The rate of defects using machine A is 5% and that using machine B Is 3%. The probability that a randomly selected item which is found defective has come from machine B is

a)   0.705                        

b)   0.24                        

c)   0.34                        

d)   cannot say                        

Question 11:- For a paired t-test using a sample of 25 the degree of freedom is

a)   23                        

b)   24                        

c)   48                        

d)   none of these                        

Question 12:- For an independent t- test a sample of 25 in each of the two groups the degree of freedom is

a)   23                        

b)   24                        

c)   48                        

d)   none of these                        

Question 13:- The sampling distribution of the mean of samples will be always normally distributed when

a)   population is normally distributed                        

b)   when sample size is large                        

c)   when population standard deviation is known                        

d)   all the above                        

Question 14:- When two attributes are tested for independence we use

a)   Z distribution                        

b)   t- distribution                        

c)   F - distribution                        

d)   Chi-square distribution                        

Question 15:- Chi-square is calculated as

a)   ∑ {(Obs-Exp)^2/Exp}                        

b)   ∑ {(Obs-Exp)/Exp}                        

c)   ∑ {(Obs-Exp)/Exp}^2}                        

d)   {(Obs-Exp)^2/Exp}                        

Question 16:- The degrees of freedom for a chi-square test with 3 columns and 2 rows is

a)   6                        

b)   5                        

c)   2                        

d)   3                        

Question 17:- Standard error for a single mean in a large sample is given as

a)   σ/√n                        

b)   σ/√n-1                        

c)   σ/√n-2                        

d)   none of these                        

Question 18:- If a variable X has a standard deviation of 10 and if all values of the variables are multiplied by 2 then the standard deviation of the new variable will be

a)   20                        

b)   4.47                        

c)   10                        

d)   none of these                        

Question 19:- If a variable X has a mean of 10 and if all values of the variables are multiplied by 2 then the mean of the new variable will be

a)   10                        

b)   20                        

c)   400                        

d)   none of these                        

Question 20:- If the mean and median of a distribution then the distribution can be said to be

a)   normally distributed                        

b)   symmetric distribution                        

c)   skewed distribution                        

d)   any of these is possible                        

Case Study

A researcher was trying to establish a relationship between height and weight of individuals. For this purpose he decided to take a random sample of 10 persons and noted their height in cms and weight in Kgs . The data is given below.:

Height in cms - 150,147,132,160,153,155,162,146,137 ,140 ;

Weights (kgs) respectively are 60,47,52,65,67,55,70,63,57,64.

The relationship is as follows:

height = 104.93 + 0.721; weight and weight = 2.33 + 0.389 height.

Question 21:- The correlation between the two variables are

a)   0.651                        

b)   0.833                        

c)   0.529                        

d)   0.78                        

Question 22:- The coefficient of determination will be

a)   0.423                        

b)   0.693                        

c)   0.608                        

d)   0.28                        

Question 23:- If the height were divided by 10 and weight kept same as before then the correlation will be

a)   0.0651                        

b)   0.529                        

c)   0.0833                        

d)   0.078                        

Question 24:- The explained variation in height based on weight is

a)   0.28                        

b)   0.35                        

c)   0.373                        

d)   0.451                        

Question 25:- The explained variation in weight based on height is

a)   0.35                        

b)   0.373                        

c)   0.451                        

d)   0.28