Statistical Reasoning Normal Approximation
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ASSIGNMENT 08
MA260 Statistical Analysis I
Directions: Be sure to save an electronic copy of your answer before submitting it to Cedar Valley College for grading. Unless otherwise stated, answer in complete sentences, and be sure to use correct English, spelling, and grammar. Refer to the "Assignment Format" page located on the Course Home page for specific format requirements.
NOTE: Show your work in the problems.
1. A recent article in the Myrtle Beach Sun Times reported that the mean labor cost to repair a color television is $90 with a standard deviation of $22. Monte's TV Sales and Service completed repairs on two sets this morning. The labor cost for the first was $75 and it was $100 for the second. Compute z values for each and comment on your findings.
2. The mean of a normal distribution is 400 pounds. The standard deviation is 10 pounds.
a. What is the area between 415 pounds and the mean?
b. What is the area between the mean and 395 pounds?
c. What is the probability of selecting a value at random and discovering that it has a value of less than 395 pounds?
3. The monthly sales of mufflers in the Richmond, VA area follow the normal distribution with a mean of 1200 and a standard deviation of 225. The manufacturer would like to establish inventory levels such that there is only a 5% chance of running out of stock. Where should the manufacturer set the inventory levels?
4. Research on new juvenile delinquents revealed that 38% of them committed another crime.
a. What is the probability that of the last 100 new juvenile delinquents put on probation, 30 or more will commit another crime?
b. What is the probability that 40 or fewer of the delinquents will commit another crime?
c. What is the probability that between 30 and 40 of the delinquents will commit another crime?
5. An Air Force study indicates that the probability of a disaster such as the January 28, 1986 explosion of the space shuttle Challenger was 1 in 35. The Challenger flight was the 25th mission.
a. How many disasters would you expect in the first 25 flights?
b. Use the normal approximation to estimate the probability of at least one disaster in 25 missions.
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Solution Summary
The statistical reasoning normal approximation is determined. A step-by-step solution is provided in the Word file attached.
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Step-by-step solutions are provided in the Word file attached.
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Education
- MSc, California State Polytechnic University, Pomona
- MBA, University of California, Riverside
- BSc, California State Polytechnic University, Pomona
- BSc, California State Polytechnic University, Pomona
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- "Hello, thank you for your answer for my probability question. However, I think you interpreted the second and third question differently than was meant, as the assumption still stands that a person still independently ranks the n options first. The probability I am after is the probability that this independently determined ranking then is equal to one of the p fixed rankings. Similarly for the third question, where the x people choose their ranking independently, and then I want the probability that for x people this is equal to one particular ranking. I was wondering if you could help me with this. "
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