1:The weights of packets of cookies produced by a manufacturer have a normal distribution with mean 202 grams and standard deviation 3 grams. What is the weight that should be written on the packet so that only 1 percent is underweight?
2:A company receives a very large shipment of components. A random sample of sixteen of these components is checked, and the shipment is accepted if fewer than two of the sampled components are defective. What is the probability of accepting a shipment containing 25% defectives?
3: You are interested in the proportion of smokers. Consider a population consisting of N = 4 elements: the first two persons smoke, while the remaining two do not smoke. That is {S, S, N, N}
(a) In this population, what is the proportion of smokers?
(b) You take a random sample of size n = 2. How many different random samples are possible?
(c) Write down the sampling distribution of P, the sample proportion of smokers in a random sample of size n = 2 from this population. That is, list the possible outcomes (sample proportions of smokers) and the associated probabilities.
(d) Calculate the mean of the sampling distribution.