Statistics and Probability Answers

Evaluate the value of the finite population correction factor when a sample of size 10
drawn from the population having size 100.

A researcher wishes to test the claim of a particular cereal manufacturer that the mean weight of cereal in the boxes is less than 300g. A sample of 50 boxes yields a sample mean weight of 296g. Assume that the population standard deviation is 5g.



Can we conclude that the claim is true? Test at α = 0.05
Obtain a 95% confidence interval for μ.

A random variable X has the probability density function given below

g(x)= {2x,0≤x<1
{ 6-x,1≤x<2
{ 0, otherwise

Show graphically and find out the probabilities: P(X≤3)

A lot consists of 10 articles, 4 with minor defects, and 2 with major defects. One
article is chosen at random. Find the probability in the following cases.
i) "The item has no defects.
ii) The item has no major defects.

Telephone company claims that the average length of local calls is 4.5 minutes.randome sample of 50 calls is observed and it was mean call length is 3.9 minutes with standard deviation of 2.8 minutes.Is sample results significantly different than claims if alpha is 0.010

The time taken to assemble a car in a certain plant has a normal distribution with mean of 25.4 hours and a standard deviation of 4.1 hours. Calculate the probability that a car can be assembled at this plant in the following period of time:

More than 28.8 hours
Between 18.6 and 27.5 hours
Between 25.0 and 34.0 hours

1). A company sells packets of durian crackers that they claim on average, contains at least 20g of durian crackers. They admit that their claim is wrong (and will refund any money), if a sample of 40 durian crackers have a mean less than 19.8g. If the standard deviation is 0.5g, determine the critical value that specifies the rejection region.

2). A researcher wishes to test the claim of a particular cereal manufacturer that the mean weight of cereal in the boxes is less than 300g. A sample of 50 boxes yields a sample mean weight of 296g. Assume that the population standard deviation is 5g.

Can we conclude that the claim is true? 1.Test at α = 0.05. [5 marks]
2.Obtain a 95% confidence interval for μ. (5marks)

Sony produces its TV sets in 3 manufacture plants A, B & C.
 Plant A produces 50% of the TV sets & the probability that a TV set
manufactured here is defective is 0.02.
 Plant B produces 30% of the TV sets & the probability of defective is 0.05.
 Plant C produces 20% of the TV sets & the probability that a TV set
manufactured here is defective is 0.01.
a) Make the probability Tree of this situation.
b) If a Sony TV is randomly selected. What is the probability that it is
defective?
c) If a TV is selected at random & found to be defective then what is the
probability that it was manufactured in plant B?