Question 1:- A sample consists of 1000 length measurements. The sample mean is 53.65 cm and the sample standard deviation is 1.25 cm. 136 measurements lie between 55.0 < x < 57.0 cm. (a) Estimate the probability (%) that a length measurement lies between 55.0 and 57.0 cm. (b) Calculate the transformed variables z, at x, = 55.0 and z, at x, = 57.0 cm. (c) Discuss why it is useful to transform from f(x) to f(z).

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Question 1:-
A sample consists of 1000 length measurements. The sample mean is 53.65 cm
and the sample standard deviation is 1.25 cm. 136 measurements lie between
55.0 < x < 57.0 cm.
(a) Estimate the probability (%) that a length measurement lies between 55.0
and 57.0 cm.
(b) Calculate the transformed variables z, at x, = 55.0 and z, at x, = 57.0 cm.
(c) Discuss why it is useful to transform from f(x) to f(z).
Question 2:-
Many voltage readings are taken from a power supply.
• The sample mean voltage reading is V = 10.12 V
• The sample standard deviation of all the readings is 0.022 V
• We assume that the errors in the readings are purely random
Write the voltage to 95% confidence level.
Transcribed Image Text:Question 1:- A sample consists of 1000 length measurements. The sample mean is 53.65 cm and the sample standard deviation is 1.25 cm. 136 measurements lie between 55.0 < x < 57.0 cm. (a) Estimate the probability (%) that a length measurement lies between 55.0 and 57.0 cm. (b) Calculate the transformed variables z, at x, = 55.0 and z, at x, = 57.0 cm. (c) Discuss why it is useful to transform from f(x) to f(z). Question 2:- Many voltage readings are taken from a power supply. • The sample mean voltage reading is V = 10.12 V • The sample standard deviation of all the readings is 0.022 V • We assume that the errors in the readings are purely random Write the voltage to 95% confidence level.
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