1. The most famous geyser in the world, Old Faithful, has a mean time between eruptions of 85 minutes. Assume the times are normally distributed with a standard deviation of 21.25 min. (a) Random samples of size n= 20 are selected from this population. Find the mean and standard deviation of the distribution of sample means, and sketch the sampling distribution, go out 3 std dev. Sketch of Sampling Distribution (b) Random samples of size n = 30 are selected from this population. Find the mean and standard deviation of the distribution of sample means, and sketch the sampling distribution, go out 3 std dev Sketch of Sampling Distribution For the next 3 questions, write out what you are putting in the calculator. (c) Find the probability that a randomly selected individual time from this population is longer than 90 minutes. ( >90)= (d) Find the probability that, for a sample of n = 20 times from this population, the sample mean is longer than 90 minutes. ( >90)= . (e) Find the probability that, for a sample of n = 30 times from this population, the sample mean is longer than 95 minutes. ( >95)=

2. According to Crown ATM Network, the amount withdrawn has a mean =$67 and standard deviation =$35. (a) Random samples of n = 50 withdrawals are selected. Find the mean and standard deviation of the distribution of sample means, and sketch this distribution, show 3 std dev. Sketch of Sampling Distribution (b) In a particular sample of n = 50 withdrawals, the sample mean withdrawal is $90. Would this be considered unusual? Explain. (Either find (>) or standardize the sample mean of $90.)