A machine is used to manufacture 3-cm nails. The lengths of 3-cm nails are normally distributed with a mean of 3.0 cm and a standard deviation of 0.09 cm. The nails that are either shorter than 2.9 cm or longer than 3.1 cm are unusable. (i) Find the percentage of all nails produced by this machine which are unusable. (ii) Find k such that 90% of the nails will have the length less than k cm. Calculate the probability that a random sample of 25 nails will have a total length of more than 76 cm. (iii)

A machine is used to manufacture 3-cm nails. The lengths of 3-cm nails are normally distributed with a mean of 3.0 cm and a standard deviation of 0.09 cm. The nails that are either shorter than 2.9 cm or longer than 3.1 cm are unusable. (i) Find the percentage of all nails produced by this machine which are unusable. (ii) Find k such that 90% of the nails will have the length less than k cm. Calculate the probability that a random sample of 25 nails will have a total length of more than 76 cm. (iii)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

A machine is used to manufacture 3-cm nails. The lengths of 3-cm nails are normally
distributed with a mean of 3.0 cm and a standard deviation of 0.09 cm. The nails that are
either shorter than 2.9 cm or longer than 3.1 cm are unusable.
(i)
Find the percentage of all nails produced by this machine which are unusable.
(ii)
Find k such that 90% of the nails will have the length less than k cm.
(iii)
Calculate the probability that a random sample of 25 nails will have a total length of
more than 76 cm.

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