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# Normal Distributions and Curves

(a) Answer true or false to each of the following statements
(i) Two normal distributions that have the same mean are centered at the same place, regardless of the relationship between their standard deviations.
(ii) Two normal distributions that have the same standard deviation have the same shape, regardless of the relationship between the means.

(b) Consider the following normal curves. Curve I (u=1.5, sigma=3), curve II (u=1.5, sigma = 6.2), curve III (u=2.7, sigma=3), and curve IV (u=0, sigma=1).
(i) Which curve has the largest speed?
(ii) Which curves are centered at the same place?
(iii) Which curves have the same shape?
(iv) Which curve is centered farthest to the left?
(v) Which curve is the standard normal curve?

(c) Sketch and determine the area under the standard normal curve that lies
(i) To the left of -3.20
(ii) To the right of 0.61
(iii) Between 1.11 and 2.75
(iv) Between -1.11 and -2.75
(v) To the right of 3.2

#### Solution Preview

a) (i) True
(ii) True

(b) (i) The curve with largest value of sigma has largest spread: Curve II (mu=1.5, sigma=6.2)
(ii) Curve I and Curve II are centred at the same place : mu ...

#### Solution Summary

Corresponding to different conditions of mean and standard deviations, some of the problems related to the normal distribution are solved.

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