Natalie had some marbles. she gave 1/3 of them to her brother, who kept 12 marbles for himself and gave the rest to 5 friends. if each friend received 7 marbles, how many marbles did natalie have at firts?

Aresearch company wants to test the claim that a new multivitamin to improve short term memory. state the objective of the experiment, suggest a population, determine the experimental and control groups, and describe a sample procedure.

Suppose that in 2008 , 840,800 citizens died of a certain disease assuming the population of teh country is 399 miliion, what is the mortality rate in units of deaths per 100,000 people?

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.