Question

The electrical resistance ? of a particular component is Normally distributed with mean 60 ohms and variance 25 ohms2. Find (i) Pr{? ≤ 65}, (ii) Pr{? > 52}; (iii) Pr{50 < ? ≤ 62}. (iv) It is required to reduce Pr{? ≤ 65} to 0.1 by changing the mean of the distribution, while keeping the variance at 25 ohms2, what is the value of the mean required?

Answer 1

We are given:

The following information has been provided:

(i)

We need to compute

The corresponding z-value needed to be computed:

Therefore,

(ii)

We need to compute

The corresponding z-value needed to be computed is:

Therefore, we get that

(iii)

We need to compute . The corresponding z-values needed to be computed are:

Therefore, we get:

(iv)

We are to find x such that:

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