Mean Absolute Deviation & Standard Deviation And The Probability - Mathematics Assignment Help

Assignment Task -

1. In a work study exercise for a hotel group a manager observed the following times, in  seconds, being taken to compile customer bills. 

155 246 255 196 366 270 172 262 262 206 

263 296 325 142 202 322 250 456 330 224 

186 112 115 127 266 266 415 316 325 292 

217 235 72 177 281 210 192 202 49 316 

261 352 256 311 346 78 441 364 211 231 

a. Draw a frequency distribution table using classes widths of 50 and from it draw a  histogram of the data. 

b. Draw a cumulative frequency diagram of the data. Using the diagram to find:

i. How many customer bills took more than 2 minutes to compile? 

ii. What is the median time taken to combine customer bills?

2. Answer the following questions (don’t just write the answer, explain with reasoning):

a. A two-stage rocket is to be launched on a space mission. The probability that the lift off will be a failure is 0.15. If the lift-off is successful, the probability that the  separation of the stages will be a failure is 0.05. If the separation is success-ful, the  probability that the second stage will fail to complete the mission is 0.02. What is the  probability that the whole mission will be a success? 

b. Suppose that out of a group of people, 20% own both a house and a car, 40% own a  house and 70% own a car. What is the probability of any person owning neither a  house nor a car? 

c. 5-member task force is to be set up to give recommendations to deal with Covid-19.  The task force is to be formed from 5 epidemiologists, 1 virologist, 2 pulmonologists, 3  modellers and 4 administrative officials. What is the probability that 2 pulmonologists  and at least 1 modeller are included in the task force?

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