Math 2201
Unit 5 Assignment
Name: ________________________
(Total Marks = Marks)
1. Find the mean median and mode of each set of data.
(A) 80, 90, 91, 76, 64, 80, 78
(B) 24, 78, 90, 87, 65, 35, 78, 90, 90, 80
2. Find the standard deviation for each data set below by using technology. (Use website
https://www.easycalculation.com/statistics/standard-deviation.php)
(A) 5,6.3,7,15.3, 8.2, 10.1, 9, 8.4, 7.8, 10.2
(B) 9,10,11,80,1,87, 60, 64, 30
(C) Why should the standard deviation in B be larger?
3. Compute the standard deviation of data set manually. Use the table method as indicated in your
notes. State the formula used.
17, 20, 89, 70, 40, 50
𝑥𝑥
𝑥𝑥̅
(𝑥𝑥 − 𝑥𝑥̅ )
(𝑥𝑥 − 𝑥𝑥̅ )2
4. Marks for the math 3201 public exam last year were as follows:
60, 90, 80, 72, 40, 44, 56, 60, 80, 78, 44, 32, 78, 66, 54, 60, 70, 65, 62, 56, 50, 54, 60, 80
(A) Using a bin width of 10 and you first class being 30 to 40, create a frequency distribution
table for the data.
(B) Sketch and label the histogram for the distribution table. Draw your frequency polygon and
use it to determine if the data are normally distributed or not.
Bin
Tally
Frequency
5. A salmon population of 500 has a mean mass of 6.4 kg with a standard deviation of 1.65 kg. Their
masses are known to be normally distributed.
(A) Draw and label a Normal distribution with all percentages.
(B) What percentage of salmon have their weight between 8.05 kg and 9.70 kg?
(C) Of the 500 salmon, how many are with two standard deviations of the mean?
(D) Determine how many salmon have a mass below 4.75 kg?
6. Draw and find the area under the curve as a decimal and percentage for the indicated z-scores
(A) z = 2.27
(B) z =-0.89
(C) Between z = -0.32 and z = 1.87
7. 1000 smart phone were recently purchased by THE SOURCE. It is known that a cell phone has a
mean life of 2.5 years with a standard deviation of 0.65 years.
(A) Draw and label a Standard Normal distribution. Compute the z-score for a phone that has a
life of 1.85 years and place the z-score on the distribution
(B) What is the probability that a phone will last less than 1.85 years? More than 1.85 years?
(Draw a diagram here as well for each case)
(C) The source would like only 10% of the phones returned. Compute the z-score for the
amount area needed on the distribution. How long of the warranty would the company
have to give if it only want 10% of its phones back.
8. In a recent survey 54% of post-secondary students indicated that they expected to earn at least
$100,000/year by the time they retire. The survey is considered accurate ±4.5% 19 times out of 20.
(A) What is the confidence interval and explain what it means?
(B) What is the margin of error?
(C) What is the confidence level?
9. A survey reports the confidence integral for a population mean is said to lie somewhere in between
70 to 90% 9 times out of ten.
(A) Compute the margin of error.
(B) What is level of confidence the interval is reported at?
(C) What percentage of time would the population mean lie outside of the indicated interval?
(D) If the sample size is increased in the survey, what effect will this have on the confidence
interval?