Factory produces whiteboard markers. The production process can be modelling by normal distribution with a mean length of 11 cm and a standard deviation of 0.25 cm. (a) What is the probability that a randomly selected whiteboard marker has a length longer than 10.5 cm? (2 marks) 100 whiteboard markers are randomly selected for quality checking. (b) What are the mean and standard deviation of the sample mean length? (2 marks) (c) What is the probability that the sample mean length will be between 10.99 cm and 11.01 cm?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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2.
Factory produces whiteboard markers. The production process can be modelling
by normal distribution with a mean length of 11 cm and a standard deviation of
0.25 cm.
(a)
What is the probability that a randomly selected whiteboard marker has a
length longer than 10.5 cm?
(2 marks)
100 whiteboard markers are randomly selected for quality checking.
(b) What are the mean and standard deviation of the sample mean length?
(2 marks)
(c)
What is the probability that the sample mean length will be between
10.99 cm and 11.01 cm?
(2 marks)
(d) If 99.8% of the sample means are more than a specific length Y, find Y.
(3 marks)
Transcribed Image Text:2. Factory produces whiteboard markers. The production process can be modelling by normal distribution with a mean length of 11 cm and a standard deviation of 0.25 cm. (a) What is the probability that a randomly selected whiteboard marker has a length longer than 10.5 cm? (2 marks) 100 whiteboard markers are randomly selected for quality checking. (b) What are the mean and standard deviation of the sample mean length? (2 marks) (c) What is the probability that the sample mean length will be between 10.99 cm and 11.01 cm? (2 marks) (d) If 99.8% of the sample means are more than a specific length Y, find Y. (3 marks)
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