







A normal distribution problem 
20140419 

From Melanie: This is the question:
The lifetime of a certain type of car tire are normally distributed. The mean lifetime of a car tire is 40,000 miles with a standard deviation of 5,000 miles. Consider a sample of 10,000 tires. A) How many tires would you expect to last between 35,000 and 45,000 miles? b) How many tires would you expect to last between 30,000 and 40,000 miles? c) How many tires would you expect to last less than 40,000 miles? d)How many tires would you expect to last more than 50,000 miles? e) How many tires would you expect to last less then 25,000 miles? f) What tires would you want on your car and explain your reasoning
Not at all sure that we've done any of this correctly and not sure how to determine how many tires will last less than 25,000 miles.
Any help is appreciated. Answered by Penny Nom. 





A normal distribution problem 
20120513 

From Alysia: The scores on a test taken by 1000 students are normally distributed with a mean of 66 and standard of deviation of 12. If the college wishes only the top 8% of people to get an A, what would the cutoff score be for the A's? Answered by Penny Nom. 





A normal distribution problem 
20101202 

From Racquel: I am stuck on this question. I am not sure if using the z score will help
me get the answer I need. Here is the question?
The average length of time per week that students at this university spend
on homework is normally distributed with a mean of 18 hours and a standard
deviation of 3 hours. If Diane spends more time on homework each week than
75% of students, what is the minimum time she must spend? Answered by Penny Nom. 





Normal Distribution 
20090902 

From Nikita: Scores on a college exam are known to be normally distributed with a standard deviation of 20. If the top 3% have scores in excess of 200, what is the mean score? Answered by Robert Dawson. 





Zscore 
20090325 

From Barb: I am having trouble finding information on a z score and the conversion to the number of standard deviations a z value can be away from the mean.
What exactly does that mean and what am I looking for?
Help Please. Answered by Harley Weston. 





A normal distribution problem 
20090321 

From EDGAR: to qualify for security officers training recruits are tested for stress tolerance. The scores are normally distributed with mean of 62 and a standard deviation of 8.
a.) If only the top 15% of recruits are selected, find the cutoff score
b.) If a candidate is rendomly selected, what is the probability that his or her socre is at least 55? Answered by Harley Weston. 





Percentiles 
20090321 

From Shawn: For a normal distribution of u=654.00 and o=138.00.
What is the percentile rank for X=426? Answered by Harley Weston. 





A normal distribution problem 
20090313 

From jude: Regarding the time it takes for an oil change has a normal distribution with a mean of 17.8 minutes and std. deviation of 5.2 minutes. A free oil change will be given to any customer that must wait beyond the guaranteed time. If they don't want to give more than 1% of its customers free oil changes how long should the guarantee be (to the nearest minute). Thank you. 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. 





Sigma in a normal distribution 
20081118 

From Justin: Suppose the random variable Y can be described by a normal curve with
Mu=40. For what value of the standard deviation is
P(20 less than or equal to Y less than or equal to 60) = 0.50
Justin Answered by Harley Weston. 





A normal distribution problem 
20081118 

From Mark: Final Averages are typically approximately normally distributed with a mean of 72 and a standard deviation of 12.5.
your professor says that the top 8% of the class will receieve an A, the next 20%, a B, the next 42%, a C and the bottom 12%, an F.
a. What average must you exceed to obtain an A?
b. What Average must you exceed to receieve a grade better than a C?
c. What average must you obtain to pass the course? (you'll need a D or better) 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. 





A normal distribution problem 
20080329 

From Lorie: 3. The amount of annual snowfall in a certain mountain range is normally distributed with a mean of 109 inches, and a standard deviation of 10 inches.
a. What is the probability that the mean annual snowfall during 40 randomly picked years will exceed 111.8 inches? Answered by Harley Weston. 





A preemployment evaluation 
20080206 

From lisa: An employer gives a preemployment evaluation to a large group of applicants.
The scores are normally distributed with a mean of 154 and a standard
deviation of 21. The employer wants to interview only those applicants
who score in the top 15%. What should the cut off score be for the interviews? Answered by Harley Weston. 





A normal distribution problem 
20071111 

From Jenny: I am a parttime student so that i have no time to ask the lecturer. moreover the book which i borrowed from state library don't have any answer. but i have already done with most of the question. but these three question which i attached is really confusing me. i am very glad that you help me. Answered by Harley Weston. 





A normal distribution problem 
20070927 

From m.j.: Car Loan Rates The national average for a new car loan was 8.28%. If the rate is normally distributed with a standard deviation of 3.5%, find these probabilities.
a. One can receive a rate less than 9%.
b. One can receive a rate less than 8%. Answered by Harley Weston. 





The weights of packages are normally distributed 
20070923 

From alan: the weight of a packet of sweets produced in a factory are normally distributed.
the mean weight is 100g
the standard deviation is 2g
all packets weighing less than 99g and more then 105g are rejected
what proportion are rejected Answered by Penny Nom. 





Standard Deviation 
20070613 

From Adrian: If you are told that the mean salary of a certain group of workers is $30,000 with a standard deviation of $4000, what proportion of workers earn over $38,000? What proportion of workers earn less than $18,000? Assume the distribution of wages is normal. Answered by Stephen La Rocque. 





Normal distribution 
20070524 

From Paula: Consider a data set that is normally distributed.
The mean of the data set is equal to 10,000.
a.) Suppose that, for this data set, 10,625 has a
"zvalue" = 2.5. Solve for the standard deviation of
the data set.
b.) Solve for the "zvalue" of 9,900. Answered by Penny Nom. 





Permutations, probability and standard normals 
20070509 

From Katrina: I have a few problems that i seem to be stuck on or can not start. Can you please help me ?
1) There are 20 people on an event planning committee. How many differnt ways can a
chairperson and assistant to the chairperson be selected?
2) An unprepared student makes random guesses for 10 true or false questions on a quiz.
Find the probability that the student passes the quiz by guessing 7 of the questions
correctly.
3) The heights of 18 year old men are normally distributed with a mean of 68 inches and
a standard deviation of 3 inches. If a random sample of 25 18year old men is selected
what is the probability that the mean height is between 68.5 and 72 inches? Answered by Penny Nom. 





A normal distributiion question 
20070420 

From Erika: The amount of time required for a certain type of automobile transmission repair at a service garage is normally distributed with the mean = 45 minutes and the standard deviation =8.0 minutes. The service manager plans to have work begin on the transmission of a customer’s car 10 minutes after the car is dropped off, and he tells the customer that the car will be ready within one hour total time. What is the probability that he will be wrong? Illustrate the proportion of area under the normal curve which is relevant in this case.
What is the required working time allotment such that there is a 75 percent chance that the transmission repair will be completed withing that time? Illustrate the proportion of area that is relevant. Answered by Penny Nom. 





A manufacturer of cotton pins 
20060320 

From Nirmal: A manufacturer of cotton pins knows that 5% of his products are defective. If he sells cotton pins in boxes of 100 and guarantees that not more than 10 pins will be defective, what is the approximate probability that a box will have the guaranteed quantity? Answered by Penny Nom. 





Another normal distribution problem 
20060218 

From Mary: Assume that blood pressure readings are normally distributed with a mean of 120 and standard deviation of 8. A researcher wishes to select people for a study but wants to exclude the top and bottom 10 percent. What would be the upper & lower readings to qualify people to participate in the study? Answered by Penny Nom. 





A normal distribution problem 
20060215 

From Mary: In a certain normal distribution, find the mean when the standard deviation is 5 and 5.48% of the area lies to the left of 78. Answered by Penny Nom. 





A normal distribution problem 
20050808 

From Brad: The life of a toy is normally distributed. Suppose 92.51% of the items lives exceeding 2,160 hours and 3.92% have lives exceeding 17,040 hours. Find the mean and the standard deviation. Answered by Penny Nom. 





Replacement times for TV sets? 
20040331 

From Barb: Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years. Estimate the probability that for 250 randomly selected TV sets, at least 15 of them have replacement times greater than 10.0 years.e Answered by Andrei Volodin and Penny Nom. 





Standard Deviation 
20031007 

From Rebecca:
I have a task to complete, which is to calculate the mean and standard deviation of something. I have done this but am then asked to write a short explanation of my findings.
I know what the mean is about, and I thought I knew what the standard deviation meant too  shows the variation from the mean. However, on a task I completed earlier the feedback I got said 'you need to tell us that it is talking about the middle 66% of the data'  that has thrown me, I don't understand that. Can anyone help me get my head round this??? Answered by Penny Nom. 





A Normal probability problem 
20021203 

From A student: The height of married men is approximately normal with mean 70 and standard deviation 3. The height of married women is approximately normal with mean 65 and standard deviation 2.5. What is the probability that a random married woman is taller than a random married man? Answered by Andrei Volodin. 





Day care 
20020513 

From Sonam: In many familes, both parents work. as a result, there is increasing need for day care. data was collected; and in one year in Canada, approximately 32% of children aged 0 to 11 years were in day care for at least 20h per week. (a) what is the probability, in a random poll of 60 children form the age of 0 to 11, that more than 15 children are in day care at least 20 h per week? nearest tenth of one %
ANSWER: P(children are in daycare at least 20h)= 60/60C14 = to the answer (b) what is the probability, in a random pool of 60 children that fewer than 20 are in day care at least 20 h per week?
ANSWER: P= 20/60= 33.3% stay in day care for 20h per week, I dont know if these answers are right please help me out. Answered by Andrei Volodin. 





Normal distribution 
20020121 

From Danielle: A teacher gave a test on which the students' marks were normally distributed, but the results were pathetic. The mean was 52% and the standart deviation was 12%. The teacher decided that the top 10% of the students should get A's, the next 20% should get B's, the next 40% should get C's, the next 20% should get D's, and the bottom 10% should get F's. To the nearest percent, what are the cutoff marks that will result in an A, B, C, D, and F? Answered by Penny Nom. 





A confidence interval 
20010628 

From Murray: An investigator wants to find out of there are any difference in "skills" between full and part time students. Records show the following:
Student Mean Score Std Dev Number
   
Full time 83 12 45
Part time 70 15 55
Compute a 95% confidence interval for the difference in mean scores. Answered by Andrei Volodin. 





Standard Deviation 
19990711 

From Anthony Fama: I have seen several answers to this question: If one standard deviation represents 68% of the population, what does two, three, four and five sigma [std deviation] represent? As stated, I have seen several different answers and thus, the impetus for my question. Answered by Harley Weston. 





The Central Limit Theorem 
19970421 

From Donna Hall: A skeptic gives the following argument to show that there must be a flaw in the central limit theorem: We know that the sum of independent Poisson random variables follows a Poisson distribution with aparameter that is the sum of the parameters of the summands. In particular, if n independentPoisson random variables, each with parameter 1/n, are summed, the sum has a Poisson distributionwith parameter 1. The central limit theoren says the sum tends to a normal distribution, butPoisson distribution with parameter 1 is not normal. What do you think of this argument? Answered by Neal Madras. 





The normal distribution. 
19970321 

From Donna D.Hall: I am looking for a proof for the normal distribution. I suppose "proof" was not a good choice of words. What I am looking for is a way to "derive" the normal distribution in simple terms so that the most average teenager can see the logic. Can you help me? Answered by Harley Weston. 

