Question

The probability distribution for the number of bacterial colonies on a square foot of kitchen can be modeled by a Binomial Distribution.

True False

The age distribution of residents in retirement communities is right skewed. The average age of residents in one very large residential retirement community is 79 years with standard deviation 5.8 years. A simple random sample of 100 residents is to be selected, and the sample mean age x̅ of these residents will be computed. We know the random variable x̅ has approximately a Normal distribution because of:

A. the population from which we're sampling has a Normal distribution

B. the law of large numbers

C. the 68–95–99.7 rule

D. the central limit theorem

Answer 1

The probability distribution for number of bacterial colonies on a square foot of kitchen can be modeled by binomial distribution so this statement is false , because here n and probability is not given and this is an Poisson distribution .Therefore given statement is False.

as the given that sample mean follows the normal distribution. When the sample size is 100 so as we know that for large sample the data goes to the normal .So here we use the Central limit theoem.

therefore the answer is Central Limit Theorem