Question

 A school caretaker looks after 6 children. The ages (in years) of the children are given below: 

 

Child Age (in years)
Meena 5
Aarav 4
Nisha 6
Kabir 4
Pooja 5

(i) What is the nature (type) of the population of the ages of children?
(ii) Construct the sampling distribution of the sample mean for all possible samples of size n = 2.
(iii) Comment on whether the sampling distribution is approximately normal.
(iv) Find the mean and standard error of the sampling distribution. (20)

24 Mar 2026
Answer :
Word Count : 366
(i) The population consists of the ages of the children: 5, 4, 6, 4, 5. The population is finite, discrete, and quantitative because it consists of a fixed number of children with specific numerical ages. (ii) To construct the sampling distribution of the sample mean for all possible samples of size (n = 2), we list all combinations of 2 children from the 5: Possible samples and their means: 1. (5, 4) → (5 + 4)/2 = 4.5 2. (5, 6) → (5 + 6)/2 = 5.5 3. (5, 4) → _________ ____ _______ _________ __________ ______ ___ ________ __________ _____ _____.
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