math
jingazama000
assignment_4.docxAssessment exercise for Assignment 4
1. From the textbook: Topic 10 Working with the normal distribution, p. 361, end-of-chapter exercise 6.53 parts (a) - (e).
From the Household Economic Survey: Year ended 30 June 2010, the average weekly household expenditure in New Zealand was $1,010 (Household Economic Survey: Year ended 30 June 2010, Statistics New Zealand ,www.stats.govt.nz>).
Assuming that weekly household expenditure is approximately Normal with standard deviation of $300: 42
(a) Find the probability that a household’s weekly expenditure is less than $500.
(b) Find the probability that a household’s weekly expenditure is more than $1,200.
(c) What proportion of household expenditures are between $750 and $1,250?
(d) 99% of households have weekly expenditures of less than what amount?
(e) 95% of households have weekly expenditures of more than what amount?
Note! For full marks, include an appropriate probability statement for each question and illustrate each calculation with an appropriate diagram. Refer to the Assignments page on the course web site for a file with diagram templates that you can copy and paste into your assignment.
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Assessment exercise for Assignment 4
2. During a university orientation event, incoming students are advised about the cost of textbooks for a typical study period. Students are told that the average student spends $280 per study period on books. Based on your own experience you feel that this is an under-estimate of the true expenditure. You ask 30 of your friends and you obtain the following textbook expenditure amounts (in dollars):
|
264 |
286 |
297 |
295 |
298 |
303 |
308 |
312 |
319 |
327 |
|
283 |
289 |
291 |
298 |
299 |
304 |
310 |
313 |
324 |
327 |
|
284 |
291 |
294 |
298 |
300 |
304 |
312 |
315 |
326 |
331 |
Assessment exercise for Assignment 4
3. A printer cartridge is reported by the manufacturer to have an average life span of 2,500 pages. A random sample of twenty-five cartridges used in a variety of printers in a company found that the mean life span was 2,410 pages with a standard deviation of 220 pages. Do you believe the company’s claim? Test at = 0.05.
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