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