Search & Filtering
A survey of all the 113 firms in a small state was carried out to find the number of people employed at
each of the sectors. The results are shown in the following table.
Number of Employees 1 – 10, 11– 20, 21 – 30, 31 – 40, 41 – 50
Frequency 35, 34, 14, 12, 18
(i) Find the mean.
(ii) Calculate the standard deviation.
(iii) Find the median.
[Verify your answer by MICROSOFT EXCEL and attach the printout]
. The Connect Internet service officer takes a sample of 30 subscribers to find out the number of hours
they spent ‘on-line’ in the last month. Here are the results:
6 9 14 15 16 17 18 21 23 24
24 27 28 33 36 37 39 39 40 40
41 43 44 45 47 48 53 57 59 63
(i) Construct a stem-and-leaf plot for the raw data.
(ii) Explain why it is likely that the underlying population of all users may have a symmetric
distribution? Give two reasons.
(iii) Construct a frequency distribution for these data, using 5 classes.
(iv) Construct a histogram and a frequency polygon for the cumulative frequency distribution.
[Verify your answer by MICROSOFT EXCEL
Given a population consists of three numbers (2,5,9).
Consider all possible samples of size 2 which can be drawn from the population.Find the standard deviation of the sampling distribution of the sample
means.
Given a population consists of three numbers (2,5,9).
Consider all possible samples of size 2 which can be drawn from the population.
Find the variance of the sampling distribution of the sample means.
The weight of baby kangaroos are known to have a mean of 125 pounds and a standard deviation of 15 pounds. If we obtained a random sample of 40 baby kangaroos what is the probability that the sample mean will be between 120 and 130 pounds and what are the confidence intervals having the same number of samples with a 95% confidence level?
We heard that there was a 90% confidence interval for the population mean from 22.5 to 2am 8.3, determine the point estimate of the population and the margin of error associated with the information.
The engine made by alpha-x for boats have an average power of 220 horsepower and a standard deviation of 15HP. You can assume the distribution of power follows a normal distribution. Beta-y is testing the engines and will dispute the company's claim if the sample mean is less than 215HP. If they take a sample of 4 engines; what is the probability the mean is less than 215? If beta-y samples 100 engines, what is the probability that the mean will be less than 215?
Assume that the time a students stays in school is normally distributed with a mean of 5 hours and a standard deviation of 0.5 hours. Every day, Clark Kent stays in school for 5.5 hours. What proportion of students stays less than 5.5 hours
The average travel time from your residence to your school is 35 minutes with a standard deviation of 10 minutes. If you want to be 99% certain that you will not be late for your first 8:00 am class, what is the latest time you should leave home? Assume that travel time is normally distributed.
The time for a major exam to be completed is normally distributed with an average of 55 minutes and a standard deviation of 9 minutes. If 92% of the students completed the exam, when should the test be terminated?
