In this article, let's discuss NPTEL Data Science for Engineers assignment answers for Week 3. The answers are 100% sure, and the proofs are provided for each question. For any queries, or further updates regarding further assignments join the telegram link provided below. 

Also Read: NPTEL Data Science for Engineers Week 2 Assignment Answers

To Join Telegram 👉 CLICK HERE

NPTEL Data Science for Engineers Week 3 Assignment 2025

Q1. Sumit wants to contact one of his friends, but he remembers only the first 9 of the 10 digits of the contact number. He is sure that the last digit of the contact number is an odd number. He selects an odd number randomly. If the random variable X denotes the last digit of the contact number, then calculate Var( X). 

A. 5
B. 8
C. 33
D. None of the above

Answer: [ 8 ] B

Q2. Suppose X∼Normal(µ,4). For n= 20 iid samples of X, the observed sample mean is 5.2. What conclusion would a z-test reach if the null hypothesis assumes µ= 5 (against an alternative hypothesis µ≠5) at a significance level of α= 0.05?

Use F−1z (0.025) = −1.9599

A. Accept H0
B. Reject H0

Answer: [ A ] Accept H0

Q3. A box contains 8 items out of which 2 are defective. A sample of 5 items is to be selected randomly (without replacement) from the box. If the random variable X represents the number of defective items in a selection of 5 items, then find E(X).(Enter the answer correct to 2 decimal places)

A. 1.25
B. 5
C. 0.4
D. 1.3

Answer: A [ 1.25]

Q4. Suppose X∼Normal(µ,9). For n = 100 iid samples of X, the observed sample mean is 11.8. What conclusion would a z-test reach if the null hypothesis assumes µ=10.5 (against an alternative hypothesis µ≠10.5)?

A. Accept H0 at a significance level of 0.10.
B. Reject H0 at a significance level of 0.10.
C. Accept H0 at a significance level of 0.05.
D. Reject H0 at a significance level of 0.05.

Answer: [ B] [ D ] 

               Reject H0 at a significance level of 0.10.

                Reject H0 at a significance level of 0.05. 

Q5. Let X and Y be two independent random variables with Var(X) = 9 and Var(Y) = 3, find Var(4X−2Y+6).

A. 100
B. 140
C. 156
D. None of the above

Answer: [ C ] 156 

Q6. The covariance between two random variables X and Y is −3.749, their variance is given by 3 and 5. Compute the correlation coefficient.

A. -0.854
B. 0.561
C. -0.968
D. None of the above

Answer: [ C ] -0.968 

Q7. When will you reject the Null hypothesis?

A. p value greater than α
B. p value less than α
C. p value equal to α
D. None of the above

Answer: [ B ]  p value less than α

Q8. A sample of N observations are independently drawn from a normal distribution. The sample variance follows

A. Normal distribution
B. Chi-square with N degrees of freedom
C. Chi-square with N−1 degrees of freedom
D. t-distribution with N−1 degrees of freedom

Answer: [ C ] Chi-square with N−1 degrees of freedom

Q9. A car manufacturer purchases car batteries from two different suppliers. Supplier X provides 55% of the batteries and supplier Y provides the rest. 5% of all batteries from supplier X are defective and 4% of all batteries from supplier Y are defective. You select a battery from the bulk and you found it to be defective. What is the probability that it is from Supplier X?

A. 0.0455

B. 0.455
C. 0.604
D. 0.018

 

Answer: [ C ] 0.604 

Q10. Which one of the following is best measure of central tendency for categorical data?

A. Mean
B. Median
C. Mode
D. None of the above

Answer: [ C ] Mode

Conclusion

All these answers are 100% sure. I ensure you check the answers from your side too. If any changes in answers, visit the telegram for faster updates or Visit the website on or before the last date.

Join Telegram 👉 CLICK HERE