What is the Central Limit Theorem? It is always true that as the sample size, n, increases, the distribution of the sample means will be approximately normally distributed. Explain

When using the central limit theorem for means with n = 98, it is not necessary to assume the distribution of the population data is normally distributed. True False

Airlines tend to overbook their flights because they assume a certain percentage of people will be 'no shows' due to change in plans or late connecting flights. A recent study suggested that 86% of people actually show up for their flight on time. A random sample of 222 booked passengers is taken and whether or not they showed up on time is recorded for each of them. The Central Limit Theorem for proportions says that the sampling distribution of the proportion of people who show up on time for their flight will have a Normal shape. (a) Give the center and standard error for the sampling distribution of proportions. Round to four decimal places as needed.   mean =  and  standard error =  (b)  What is the probability that at least 88% of the randomly selected booked passengers showed up on time?       P(ˆp ≥0.88)= (c) What is the probability that between 82% and 90% of the randomly selected booked passengers showed up on time?  P(0.82≤ˆp ≤0.9)= (d) Is 83% an unusually low percentage of…

The central limit theorem states that the sampling distribution of sample means has a mean equal to the population --     mean  mean   mean divided by the population standard deviation   mean divided by the population standard deviation  standard deviation  standard deviation  standard deviation divided by the square root of N.