Statistics and Probability Answers

Research objective: The population mean is greater
than 7.5.
σ = 1.5, n = 30, x = 8.5

A manufacturing firm produces pipes in two plants I and II with daily production 1,500 and 2,000 pipes respectively. The fraction of defective pipes produced by Plants I and II are 0.006 and 0.008 respectively. If a pipe selected at random from the days production is found to be defective, what is the probability that it has come from plant I, Plant II ?

Set up a 95% confidence interval estimate for the population mean, based on each of the
following sets of data, assuming that the population is normally distributed:
Set 1: 1, 1, 1, 1, 8, 8, 8, 8
Set 2: 1, 2, 3, 4, 5, 6, 7, 8
Explain why these data sets have different confidence intervals even though they have the
same mean and range.

Prepare for a data collection as follows:

Each of the team members is required to unwrap 3 packs of 45g of ‘Skittles original fruity candy’.



Count the number of candies with the same colour in each pack.
Let X be the number of red candies in each pack. Count the number of RED candies in each pack (e.g. 5, 4, 7: see TABLE 1).
Record the data obtained as in TABLE 1, TABLE 2 AND TABLE 3 below.

TABLE 1: Number of candies by colour and by team member
Colour
Member no.1
Member no. 2
Member no. 3
Member no. 4
Member no. 5
Total
green












yellow












red
5+4+7 = 16










orange












purple












Total












(3 Marks)

. If X and Y are independent chi-square variates with n1 and n2 d.f. respectively. Show
that U = X + Y and V = n2X/n1Y are independently distributed. Also indentify their
distributions

Let {Xn} be a sequence of independent Bernoulli variates such that
P (Xn = 1) = pn , P (Xn = 0) = 1- pn = qn , n = 1,2,3,…………..
Examine whether the weak law of large numbers and central limit theorem can be
applied to the sequence {Xn}.

Research objective: The population mean is not
equal to 1,500.
σ = 220, n = 125, x = 1525

A shipment of 15 similar microcomputers to a retail outlet contains 5
that are defective. If a school makes a random purchase of 4 of these
computers, find the probability distribution and the expectation for the
number of defective items.

Baby Rachel wants to arrange 9 blocks in a row. How many different arrangements can she make?

ow many different ID cards can be made if there are 6 digits on a card and no digit can be used more than once?