Question

In: Statistics and Probability

Assume that you have a box of resistors that have a Gaussian distribution of resistances with...

Assume that you have a box of resistors that have a Gaussian distribution of resistances with mean µ = 100 Ω and standard deviation σ = 20 Ω
(i.e., 20% resistors). Suppose that you wish to form a subgroup of resistors
with µ = 100 Ω and standard deviation 5 Ω (i.e., 5% resistors) by selecting all resistors with resistance between the two limits r1 = µ−a and r2 = µ+a.
(Apparently, you are too cheap to just order the resistors with the appropri-
ate resistance tolerance from Mouser.)

(a) Find the value of a.

(b) What fraction of resistors should satisfy the condition?

(c) Find the standard deviation of the remaining sample.

Solutions

Expert Solution

Here 5% of the resistors mean we need to compute the confidence interval for the given parameters using normal distribution.

We assume that the n = 1000

Following are the calculations for the same,

Value of a = 0.31

b) Almost, 95% of the population will fall into this group

c) Std dev of the remaining sample = sigma/(0.05*n)

orchestra answered 2 years ago
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