Statistics and Probability Answers

a. In a butter-packing plant, the quality of butter packed in a day using a certain type of machine is normally distributed with mean and variance 4. On a particular day, 12 packets of butter were taken at random from this production line and their masses, measured in grams, were:
9.5 11.2 9.9 10.9 10.1 10.9
9.5 10.6 11.1 9.8 10.2 11.0
Find a 97% confidence interval for the mean mass produced by this machine.
Explain the answer.

b. What sample size would be required to estimate the population mean for a large file of invoices of a multinational company to within RM0.50 with 95% confidence, given that the estimated standard deviation of the value of the invoices is RM6?

7. Property taxes for an Ontario resident over the years are listed.

Year: 2007 2008 2009 2010 2011 2012

Taxes: $2,900 $3,000 $3,150 $3,300 $3,400 $3,600

b) Calculate the least squares equation. (4 marks)
c) Predict the property tax for the year 2020. (2 marks)

Question 1. The average rate of emission radioactive particles from a source was measured over a long period, and found to be 10 particles per unit time. After an experimental treatment had been applied to the source, a further sample was examined and emitted 17 particles in unit time. Test at 5% the null hypothesis that the rate of emissions is unchanged.

The weight of 500 college students is 70 kg and the standard deviation is 3 kg. Assuming that the weight is normally distributed, determine how many students weigh: between 60 kg and 75 kg, more than 90 kg, less than 64 kg, exactly 64 kg

A machine elastic bands with breaking tension normally distributed with mean 45 N and
standard deviation 4.36 N.
a. In order to test whether there is a change in the mean breaking tension, a random
sample of 50 was tested and found to have a mean breaking tension of 43.46 N.
i. Determine a 95% confidence interval for the population mean breaking tension
based on the sample mean assuming an unchanged standard deviation.
ii. Make a conclusion for answer (a)(i).
b. If the standard deviation has changed to sigma, find the least value of sigma
for a 95 % confidence interval for the population mean to contain 45 N.

Find the probability N?
No 4 on first die
No 4 on any of the die
No 3 on the 1 die and 5 on the 2 die
3 and 5 on any of the die
Difference between no is 2

A man can go by any of the 5 buses and will return by any of the remaining 4 buses ?

Find the permutation of 4 objects A,B,C,D taken 2 at a time?

In how many ways a committee of 3 students can be selected from 4 students A,B,C,D ?