Question

3. A company manufactures square boards for the DIY trade. The length of side of each board is normally distributed with mean 1.5m and standard deviation 5mm, independently of all other boards. i. What is the probability that the area of a randomly chosen board will be less than $2.24m^2$? ii. Find, approximately, the probability that among 60 such boards, more than 10\% will have areas under $2.24m^2$.

          3. A company manufactures square boards for the DIY trade. The length of side of each board is normally distributed with mean 1.5m and standard deviation 5mm, independently of all other boards.
i. What is the probability that the area of a randomly chosen board will be less than $2.24m^2$?
ii. Find, approximately, the probability that among 60 such boards, more than 10\% will have areas under $2.24m^2$.

3. A company manufactures square boards for the DIY trade. The length of side of each board is normally distributed with mean 1.5m and standard deviation 5mm, independently of all other boards.
i. What is the probability that the area of a randomly chosen board will be less than 2.24m^2?
ii. Find, approximately, the probability that among 60 such boards, more than 10% will have areas under 2.24m^2.

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Krishna G

Step 1

We need to find the probability that a randomly chosen square board has an area less than 2.24 square meters. The side length of the boards follows a normal distribution with a mean of 1.5 meters and a standard deviation of 5mm (or 0.005 meters). We also need to Show more…

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A company manufactures square boards for the DIY trade. The length of side of each board is normally distributed with mean 1.5m and standard deviation 5mm, independently of all other boards. i. What is the probability that the area of a randomly chosen board will be less than 2.24m^(2) ? ii. Find, approximately, the probability that among 60 such boards, more than 10% will have areas under 2.24m^(2). 3. A company manufactures square boards for the DIY trade.The length of side of each board is normally distributed with mean 1.5m and standard deviation 5mm independently of all other boards. i. What is the probability that the area of a randomly chosen board will be less than 2.24m2? ii. Find, approximately, the probability that among 60 such boards, more than 10% will have areas under 2.24m2