statistics mathematical problems
By lovelybc
@lovelybc (15)
Bahamas
December 18, 2007 7:36pm CST
Can anyone provide the solutions to these problems?
1.The mean and standard deviation of the gross weekly income distribution of a local company's 150 employees were determined to be $170 and $10 respectively. Approximately what percentage of the employees would be expected to have incomes over $190 per week? Under $160 per week? If you were employed by this company and your weekly income was $185, how many standard deviations would your salary be away from the mean salary? What would your Z-score then be?
2. A company that bottles soda has determined that it lost an average of 30.4 cases per week last year due to breakage in transit. The standard deviation of the number of cases lost per week was 3.8 cases. With only this information, what can you say about the number of weeks last year that the company lost more than 38 cases due to breakage in transit? Justify your answer.
3. The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 8,300 miles. If the manufacturer warrants the tires for the first 45,000 miles, what proportion of the tires will be replaced under warranty? What if the warranty is for the first 40,000 miles?
4. Salaries for a Computer tech company for 2006 are listed below:
7.88M, 7.70M, 4.20M,6.6M, 6.19M, 920K
5.37M, 1.35M, 870K, 760K, 950K, 4.16M
2.65M, 1.97M, 5.22M, 720K, 1.61M, 720K
3.55M, 1.65M, 1.58M, 810K, 850K, 470K
600K, 590K, 340K, 510K, 470K, 850K
400K, 600k, 390k, 450k, 370k, 1.66M
280k, 950k, 990k, 720k, 1.30m, 410k
580k, 300k, 300k,. 440k, 270k, 540k
960k, 460k, 290k
a. Display the frequency distribution of the salaries graphically in a histogram (choose intervals to use along the horizontal axis) and tell what is the mean, median and skew of the distribution.
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1 response
@jormungand (91)
• Turkey
2 Jan 08
Hmm, you actually want someone to make your whole homework, even draw a frequency distribution table? That's clever!
I'll not mess with the others but I can explain the question 2.
If the distribution is normal, 95% of the values are within two standard deviations. In this case, within 30.4-(2*3.8) and 30.4+(2*3.8), equals within 22.8 and 38. So, we have 5% remaining. Half of this is under 22.8, and the other half is above 38. So the answer is 2.5%.
Hope it helps.