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Sacks of potatotes are packed by an automatic loader with mean weight 114 lb. in a test it


was found that 10% bags were over 116 lb. use this to find the SD of the process. If the


machine is now adjusted to a mean weight of 113 lb, what percent are now over 116lb, if


SD remains unaltered?


13) In a soap making process it was found that 6.23


% of bars produced weighed less than 90.50


g and 4% weighed more than 100.25 g


a. Find the mean and the S.D. of the process.


b. What percent of the bars would you expect to weigh less than 88g?


14) A light bulb manufacturer finds that 5% of his bulbs last more than 500 hours. An


improvement in the process meant that the mean lifetime was increased by 50 hours. In a


new test, 20% of bulbs now lasted longer than 500 hours. Find the mean and standard


deviation of the original process.


Buoyancy aids in watersports are tested by adding increasing weights until they sink. A


club has two sets of buoyancy aids. One set is two years old, and should support weights


according to 𝑁(6.0,0.64)kg, the other set is five years old and should support weights of


𝑁(4.5, 1.0) kg. all the aids are tested and any which are unable to spport at least 5kg are


thrown out.


a. If there are 24 two-year aids, how many are still usable?


b. If there are 32 five-year old aids how many are still usable?

QUESTION III


A short term insurance company receives three motor vehicle claims, on average, per day. Assume that


the daily claims follow a Poisson process.


Required:


a) What is the probability that at most two motor vehicle claims are received in any given day?


b) What is the probability that more than two motor vehicle claims are received in any given period


of two days?

An insurance company found that 45% of all insurance policies are terminated before their maturity







date. Assume that 10 polices are randomly selected from the company’s policy database. Assume a







Binomial experiment.







Required:







a) What is the probability that eight policies are terminated before maturity?







b) What is the probability that at least eight policies are terminated before maturity?







c) What is the probability that at most eight policies are not terminated before maturity?

Given ΞΌ = -10, Οƒ = 5, n=500, find πœ‡π‘‹Μ… and 𝜎 2 𝑋̅ Solution

Given ΞΌ = -10, Οƒ = 5, n=500, find πœ‡π‘‹Μ… and 𝜎 2 𝑋̅ Solutio

Using polar coordinates find if the limit does or does not exist for


Lim(x,y)approaches(0,0) (2x/(x^2+X+y^2))

The cost of two tables and three chairs is Ghc 705. If the table costs

Ghc 40 more than the chair, find the cost of the table and the chair.



The amount of material used in making a custom sail for a sailboat is normally distributed with a standard deviation of 64 square feet. For a random sample of 15 sails, the mean amount of material used is 912 square feet. Find a 90% confidence interval for the population mean amount of material used in a custom sail.

  1. Point estimate value =Β 
  2. Standard error (approximate to four decimal points) =Β 
  3. Margin of error (approximate to four decimal points) =Β 
  4. Tabulated value (approximate to four decimal points) =Β 
  5. Upper limit (approximate to four decimal points) =Β 
  6. Lower limit (approximate to four decimal points) =Β 
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