Sandpaper is rated by the coarseness of the grit on the paper. Sandpaper that is more coarse will remove material faster. Jobs such as the final sanding of bare wood prior to painting or sanding in between coats of paint require sandpaper that is much finer. A manufacturer of sandpaper rated 220, which is used for the final preparation of bare wood, wants to make sure that the variance of the diameter of the particles in their 220 sandpaper does not exceed 2.0 micrometers. 41 randomly selected particles are measured. The variance of the particle diameters is 2.14 micrometers. Assume that the distribution of particle diameter is approximately normal. Required:
a. Construct the 90% confidence intervals for the population variance and standard deviation.
b. Test at a 5% significance level whether the variance of the particle diameters of all particles in 220-rated sandpaper is greater than 2.0 micrometers

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step-by-step explanation:

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step-by-step explanation:

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fabric (square meters)                   cloaks

7                                                           21

4/3                                                         4

step-by-step explanation:

we are told that harry needs 2 square meters of fabric for every 6 wizard cloaks he makes.

1. first of all we will find how many cloaks can be made from 1 square meter of fabric by dividing 6 by 2.

we can see that 3 cloaks can be made from 1 square meter of fabric. now we will multiply 3 by 7 to find number of cloaks made from 7 square meters of fabric.

therefore, harry will make 21 cloaks from 7 square meters of fabric.

2. let us find how many square meters of fabric will be needed to make 4 cloaks.

first of all we will find fabric needed for 1 cloak by dividing 2 by 6.

we can see that fabric needed for 1 cloak is   square meter. now we will multiply   by 4 to find fabric needed for 4 cloaks.