For the population whose distribution is Exponential with decay parameter $M=0.15$, random sample of size $n=36$ are repeatedly taken. Compute $\mu$ and round to two decimals. Use this value to find the following. Answers of 0 and 1 are possible due to rounding. a. $P(6.17<\bar{x}<7.07)$ : (to 4 decimals) b. The 40 th percentile for sample means: (to 1 decimal)

Step 1 ：We are given that the decay parameter of the exponential distribution is \(M = 0.15\).

Step 2 ：The mean of an exponential distribution is given by \(\mu = \frac{1}{\lambda}\), where \(\lambda\) is the decay parameter.

Step 3 ：Substituting \(\lambda = M = 0.15\) into the formula, we get \(\mu = \frac{1}{0.15}\).

Step 4 ：Calculating the above expression, we find that \(\mu = 6.67\).

Step 5 ：\(\boxed{6.67}\) is the mean of the exponential distribution with decay parameter \(M = 0.15\).