A light bulb manufacturer claims that a certain type of bulb they make has a mean lifetime of 1000 hours and a standard deviation of 20 hours. Each package sold contains 4 of these bulbs. Suppose that each package represents an SRS of bulbs, and we calculate the sample mean lifetime \bar x x ˉ x, with, \bar, on top of the bulbs in each package. 1. What is the null and alternative hypotheses? 2. At a = .02, do you have enough evidence to reject the manufacturer's claim?

The owner of the plant nursery where you were tells you to fill 350 ml bottles from a 30 l from a fertilizer

Jake bakes and sell apple pies. he sells each pie for $5.75 . the materials to make the pies cost $40. the boxes jake puts the pies in cost & 12.50 total. how many pies does jake need to sell to earn a profit of $50

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.