The weight of female goats is Normally-distributed with a me…

The weight of female goats is Normally-distributed with a mean of 145 lbs. and a standard deviation of 9 lbs. Now you take a random sample of 8 goats and find that their sample mean is 139 lbs. with a sample standard deviation of 11 lbs. What is the probability that the sample mean is between 139 and 145 lbs?

A laboratory blood test has 97% sensitivity, that is, 97% ef…

A laboratory blood test has 97% sensitivity, that is, 97% effective in detecting a certain disease when it is in fact present. However, the test also yields a “false positive” result for 1% of the healthy persons tested. If 2% of the population actually has the disease, what is the probability that a person has the disease given that the test result is positive?

An unusual gene from a Eukaryotic protozoan parasite that ca…

An unusual gene from a Eukaryotic protozoan parasite that cause human diseases contains a “group I intron” that must be spliced out to form a mature mRNA that encodes a protein. If the entire exact DNA sequence (including the group I intron) for this gene is inserted into a prokaryote genome like E. coli, when E. coli tries to express this gene the resulting polypeptide sequence will be the same as when it is made in the parasite.