Quantitative Methods – I June 2025 Solved Assignments

Description

Course: Quantitative Methods – I

NMIMS Centre for Distance and Online Education (NCDOE)
Internal Assignment Applicable for Jun 2025 Examination

Q1 From a large batch of batteries, a sample of size 50 is drawn. The average lifespan of the batteries is 1200 hours with a standard deviation of 200 hours.
1. Find the probability that the mean lifespan of the sample is less than 1150 hours. (3 Marks).
2. Calculate the 95% confidence interval for the sample mean lifespan. (4 Marks)

3. Discuss the effect of increasing the sample size to 100 on the standard error and the probability calculation. (3 Marks)
(10 Marks)

Introduction
This analysis focuses on calculating the probability that the mean lifespan of a sample of batteries is less than a specified value, determining the 95% confidence interval, and examining the impact of increasing the sample size on the standard error and probability. The given problem involves a large batch of batteries where a sample of 50 is drawn. The average lifespan of the batteries is 1200 hours, with a standard deviation of 200 hours. We aim to find the probability that the sample mean lifespan is less than 1150 hours and then calculate the 95% confidence interval. Additionally, we discuss how increasing the sample size to 100 affects the standard error and probability.

Q2 (A) A deck of cards contains 10 red and 6 black cards. If two cards are randomly drawn without replacement, what is the probability that both cards drawn are black?
What is the probability that at least one of the two cards drawn is red? Total 5 Marks
(5 Marks)

Q2 (B) A milling machine is set to produce rods that have an average length of 15.00 cm. The machine is known to have a standard deviation () of 0.3 cm. The customer specifies the rod length to be within 14.80 cm and 15.20 cm.

What is the acceptance percentage given the setting and age of the machine (age determines the standard
deviation)? (5 Marks)

 

Solution:
To determine the acceptance percentage of rods produced by the milling machine, we use the normal distribution properties. The machine produces rods with a mean length (μμ) of 15.00 cm and a standard deviation (σσ) of 0.3 cm. The customer requires rods to be between 14.80 cm and 15.20 cm.

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