







Two spinners 
20180813 

From Atina: A spinner has four equal sectors and a number is written on each sector; 1, 2, 3 and 4. A twodigit number is formed by spinning two times. The number on the first spinning makes the first digit and the number on the second spinning makes the second digit. For example, 2 on the first spinning and 1 on the second spinning make the number 21.
(a) Give the sample space S for the experiment.
(b) Consider the following events : E = odd number; F = number smaller than 35; G = prime number.
Give the subset of outcomes in S that defines each of the events E, F, and G.
(c) Describe the following events in terms of E, F, and G and find the probabilities for the events.
• getting an even integer less than 35.
• getting an odd number or an prime.
• getting an even number greater than or equal to 35 that is a prime number. • an odd number smaller than 35 that is not a prime number.
(d) Are E and F mutually exclusive events? Give a reason for your answer. Answered by Penny Nom. 





Percentage of water in a soil sample 
20120301 

From avi: what i need is the formula in getting the percentage from gram.
situation:
i need to know how many percent will i declare in getting the moisture of a soil sample
i weighed 2,000 grams of soil before i dried it out in the oven, after few hours the recovery
of the dried out soil is 1,700 grams. How many percent will be the water content?
kindly send me a formula in computing this.
thank u very much! Answered by Penny Nom. 





Sample size 
20100329 

From Rae: What sample size was needed to obtain an error range of 2% if the following statement was made? "75% of the workers support the proposed benefit package. These results are considered accurate to within + or  2%, 18 out of 20 times. This seems like a straight forward question but I'm getting it wrong. Could you please help me out even just the set up would be appreciated so I can see if that's where I'm going wrong. Thanks Answered by Harley Weston. 





Sample variance 
20100125 

From shodhan: A series of 100 measurements of a physical quantity have been made that show a random fluctions characterized by a sample variance of 2% of teh mean value. If the series is lengthed to 1000 measurements made under the same conditions, estimates the sample variance of the larger set of data. Answered by Robert Dawson. 





The distribution of sample sums 
20081121 

From Mark: For large samples, the sample sum (Σ x) has an approximately normal distribution.
The mean of the sample sum is n*μ and standard deviation is (σ*√n). The distribution of savings per account for savings and loan institution has a mean equal to $750 and a standard deviation equal to $25. For a sample of 50 such accounts, find the probability that the sum in the 50 accounts exceeds $38,000. Answered by Penny Nom. 





Sample variance: inches to centimeters 
20080922 

From Anita: The average height of a sample of basketball players is 6 feet, 2 inches or 74 inches.
The standard deviation of this sample of players is 4 inches. If each person's height were to be multiplied by 2.54, what would be the value of the resulting sample variance? Answered by Harley Weston. 





zscore 
20080702 

From Candace: If a normalshaped distribution has a mean of 80 and a standard deviation of 15 what is the zscore for M=84 for a sample of n=25 scores. Is this sample mean in the middle 95% of the distribution? Answered by Harley Weston. 





The distribution of sample means 
20080702 

From crystal: A population forms a normal distribution with a mean of 75 and a standard deviation of 20. How do I sketch the distribution of sample means for samples of n= 100? Answered by Harley Weston. 





Sample variance and population variance 
20070922 

From Willy: I have a question in sample variance and population
my name is Willy the question in the attached file... Answered by Harley Weston. 





Sample size 
20070717 

From Nurse: If a population has standard deviation 20, what is =
the
minimum sample size to be 95% confident that the error should be =
accurate to
within 4? Answered by Harley Weston. 





Find the sample size needed 
20070513 

From Mini: Find the sample size needed to be 98% confident thata marketing survey on the proportion of shoppers who use the internet for holiday shopping is accurate within a margin of error of 0.02. Assume that the conditions for a binomial distribution are met, and that a current estimate for a sample proportion does not exist. Answered by Penny Nom. 





All samples of size 3 
20070419 

From Liz: Consider the population of the first seven integers: 1, 2, 3, 4, 5, 6, and 7; N=7. For this population, mean = 2 and standard deviation = 2.
a. How many samples of size three can be extracted from this population (sampling without replacement)?
b. Form the complete set of samples of size three and for each sample, compute the sample mean and median. Answered by Penny Nom. 





Choosing a bicycle 
20070328 

From Jackie: A specific brand of bike comes in two frames, for males or females. Each frame comes in a choice of two colors, red and blue, and with a choice of three seats, soft, medium, and hard.
a) Use the counting principle to determine the number of different arrangements of bicycles that are possible.
b) Construct a tree diagram illustrating all the different arrangements of bicycles that are possible. c) List the sample space. Answered by Penny Nom. 





A sample size estimation 
20051203 

From Ivonne: I have to do a research about the behavior of library users. We are going to apply a survey to a population of 1280 students (Management an Economics students) but of course we have to do it to a sample....I need to know the size of my sample. Answered by Penny Nom. 





Two word problems 
20051114 

From Jennifer:
1. Every other person on a school's parent advisory committee is surveyed to determine how many people support passage of a school bond to build a new elementary school. Is this a good sample? Why or why not?
2.What is the difference in elevation between the highest point in California,Mount Whitney,which towers 4421 meters above sea level, the lowest point in California,Death Valley, which lies 86 meters below sea level?
Answered by Harley Weston. 





A random sample 
20051016 

From Stu: If I have a set of data points (14 to be exact)of unknown pedigree from a large population, what tests can I apply to see if they constitute a random sample from the large population? Answered by Andrei Volodin and Penny Nom. 





Means of sample means 
20051012 

From Fareeha: A population consists of six numbers 1,2,3,4,5,6
a) How many different samples of two numbers can be selected with replacement? and list them.
b) Calculate the mean and standard deviation of the population
b2) Calculate the mean and standard deviation of the mean of the samples.
c) Find the standard error of your estimated mean in question b2 and compare with the estimated standard deviation in b2. Answered by Penny Nom. 





Sample variance 
20050817 

From Rosalie: To give an unbiased estimate of the population variance, the denominator of the sample variance should be (n1) instead of n. I tried to convince myself by comparing the population variance and sample variance (with denominator n and n1): Answered by Penny Nom. 





X bar 
20031104 

From mary: Remind me what this means:
_
X
Answered by Andrei Volodin. 





A sample size problem 
20011028 

From Charles: The U.S Transportation Dept. will randomly sample traffic reports to estimate the proportion of accidents involving people over the age of 70. The Dept. has no advance estimate of this proportion. how many reports should the dept select to be atleast 97% confident that the estimate is within .01 of the true proportion? Answered by Harley Weston. 





Central Limit Theorem and Law of Large Numbers 
20000626 

From Jonathan Yam: The Central limit Theorem states that when sample size tends to infinity, the sample mean will be normally distributed. The Law of Large Number states that when sample size tends to infinity, the sample mean equals to population mean. Is the two statements contradictory? Answered by Paul Betts and Harley Weston. 





Sample variance 
20000416 

From Jonathan Freeman: I was just reading your article entitled "A Note on Standard Deviation" I'm now teaching a unit on s.d. and my students were wondering why one uses a denominator of n for a population and n1 for a sample. I saw in your article that this is because "[the quantity] tends to underestimate sigma... and other technical reasons." To which my students again asked... "Why?" Could you please elaborate a bit on the "other technical reasons" perhaps in terms a high school senior (or their teacher...) could understand? Answered by Harley Weston. 





Random 
19980915 

From Hugh Ballantyne: I am an occasional teacher. Here is my question: Does the word "random" have a technical meaning in mathematics? Answered by Harley Weston. 

