1. 7.2 Notes Central Limit Theorem

2. Theorem 7.1 – Let x be a normal distribution with mean μ and standard deviation σ. Let be a sample mean corresponding to random sample of size n. http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/

3. Ex. 1 Pinedale fishing pond has trout whose lengths are normally distributed with mean μ = 10.2 in. and standard deviation σ = 1.4 in. a)What is the probability that a single trout chosen at random is between 8 and 12 in.? b)What is the probability that of 5 trout chosen at random is between 8 and 12 in.? c)Are the two values the same? Why or why not?

4. Central Limit Theorem – If x possesses any distribution with mean μ and standard deviation σ, then the sample mean based on random sample size of n will have a distribution that approaches normal with and as n approaches. ∞ http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/ The essential question is “How large does n have to be to approximate normal?”

5. Ex. 2 Let x be the bacteria count per ml of raw milk with μ = 2500 and σ = 300. A health inspector takes 42 random samples of the raw milk produced each day. At the end of each day, the bacteria count in 42 samples is averaged to obtain. a)What can we say about distribution? b)What is the probability that the average bacteria count for one day is between 2350 and 2650 bacteria per ml? c)What is the probability that the average bacteria count for one day is greater than 2650?

6. *Ex. 3 Taxi and takeoff time for commercial jets has μ = 8.5 min. and σ = 2.5 min. Assume the jets are lined up on a runway so that one taxis and takes off immediately after the other. What is the probability that for 36 jets on a given runway, the total taxi and takeoff time will be less than 320 min.?

7. Assignment Day 1 p. 306 #4, 9, 11, 15, 19 Day 2 p. 306 # 6, 8, 12, 13, 16, 20