The coefficient of variation (CV) for a sample Y₁, Y₂, ..., Y_n is defined by CV =S/Y . This quantity, which gives the standard deviation as a proportion of the mean, is sometimes informative. For example, the value S = 10 has little meaning unless we can compare it to something else. If S is observed to be 10 andY is observed to be 1000, the amount of variation is small relative to the size of the mean. However, if S is observed to be 10 andYis observed to be 5, the variation is quite large relative to the size of the mean. If we were studying the precision (variation in repeated measurements) of a measuring instrument, the first case (CV = 10/1000) might provide acceptable precision, but the second case (CV = 2) would be unacceptable.

Let Y₁, Y₂, ..., Y₁₀ denote a random sample of size 10 from a normal distribution with mean 0 and variance ². Use the following steps to find the number c such that

P(cS/Yc)=0.95

1. Find the distribution of10Y2/S2.

1. Find the distribution ofS2/10Y2.

1. Use the answer to (b) to find the constant c.