Thompson and thompson is a steel bolts manufacturing company. their current steel bolts have a mean diameter of 140140 millimeters, and a standard deviation of 88 millimeters. if a random sample of 4949 steel bolts is selected, what is the probability that the sample mean would be greater than 141.4141.4 millimeters? round your answer to four decimal places.

Tan198=asin164=? how to solve this? ?

Analyze the diagram below and complete the instructions that follow. how to find tan

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.