Question

Bacteria can develop resistance to antibiotics. To understand what can be treated, a scientist has collected data on values that inhibit the growth of a certain bacteria. It is known that the amount of drug needed, ?, has a Normal distribution with a mean of 5 mg and a standard deviation of 1.1 mg.

a) What is the probability ? is greater than 5.5 mg?

b) Given that the amount of drug is between 5 mg and 6 mg, what is the probability that it is less than 5.5 mg?

c) For the purpose of monitoring resistance, the scientist wants to know the 99th percentile of ?. Find it.

d) Without using the Z-table, find the 16th percentile. (Use the EMPIRICAL RULES on this.)

e) Without using the Z-table, what is the probability ? is between 2.8 and 6.1? (Use the EMPIRICAL RULES on this.)

f) The scientist realizes there is measurement error in his experiment referred to as ?. The measurement error is independent of ?. Through her collaborators, the scientist learns that ?~??????(? = 0,? = 0.5). What are the distribution, and parameters of ?+??

Answer 1