Tutors Answer Your Questions about Density-curves-and-normal-distributions (FREE)
Question 1180015: Suppose 200 people are lined up side-by-side, each one holding a fair coin. Each person flips their coin 64 times; every time it lands heads they step 1 meter forward, each time it lands tails they step 1 meter backward. Use a normal approximation to answer the following question: after everyone finishes their 64 steps, approximately how many people will be standing between 4 and 8 meters behind the starting line?
Click here to see answer by ikleyn(52781)   |
Question 1180015: Suppose 200 people are lined up side-by-side, each one holding a fair coin. Each person flips their coin 64 times; every time it lands heads they step 1 meter forward, each time it lands tails they step 1 meter backward. Use a normal approximation to answer the following question: after everyone finishes their 64 steps, approximately how many people will be standing between 4 and 8 meters behind the starting line?
Click here to see answer by CPhill(1959)  |
Question 1186329: A random variable is normally distributed. It has a mean of 245 and a standard deviation of 21.
a.) If you take a sample of size 10, can you say what the shape of the distribution for the sample mean is? Why?
b.) For a sample of size 10, state the mean of the sample mean and the standard deviation of the sample mean.
c.) For a sample of size 10, find the probability that the sample mean is more than 241.
d.) If you take a sample of size 35, can you say what the shape of the distribution of the sample mean is? Why?
e.) For a sample of size 35, state the mean of the sample mean and the standard deviation of the sample mean.
f.) For a sample of size 35, find the probability that the sample mean is more than 241.
g.) Compare your answers in part c and f. Why is one smaller than the other?
Click here to see answer by CPhill(1959) |
Question 1186331: The mean cholesterol levels of women age 45-59 in Ghana, Nigeria, and Seychelles is 5.1 mmol/l and the standard deviation is 1.0 mmol/l (Lawes, Hoorn, Law & Rodgers, 2004). Assume that cholesterol levels are normally distributed.
a.) State the random variable.
b.) Find the probability that a woman age 45-59 in Ghana has a cholesterol level above 6.2 mmol/l (considered a high level).
c.) Suppose doctors decide to test the woman’s cholesterol level again and average the two values. Find the probability that this woman’s mean cholesterol level for the two tests is above 6.2 mmol/l.
d.) Suppose doctors being very conservative decide to test the woman’s cholesterol level a third time and average the three values. Find the probability that this woman’s mean cholesterol level for the three tests is above 6.2 mmol/l.
e.) If the sample mean cholesterol level for this woman after three tests is above 6.2 mmol/l, what could you conclude?
Click here to see answer by CPhill(1959) |
Question 1194450: Yuen Zhi is running a ring toss event at the school fair. In the event, each attempt has a 15% chance of winning a prize. She has 45 prizes and believes that 250 people will attempt the event. She is worried that she won't have enough prizes. Based on the information provided, can Yuen be at least 95% confident that she will she have enough prizes for the event?
Click here to see answer by yurtman(42) |
Question 1194474: We have been using the normal distribution to approximate situations that are, in fact, binomial events. Create an example of a binomial event that can be approximated by a normal distribution and:
a)Demonstrate how accurate the approximation is by using both approaches to find the probability of the same event. Hint: Calculate the probability of the event as a binomial (sum of all binomial events) and calculate the probability of the approximated event using a normal distribution, and compare them to see how close the approximation is.
b)Describe the conditions under which the normal distribution would give a less accurate approximation.
c)Explain a situation in which the criteria for using the normal approximation would be met, i.e.np≥5 and n(1-p)≥5, and yet you would decide not to use the normal distribution.
Click here to see answer by yurtman(42) |
Question 1204994: In a factory that produces wire, the spooling machine is programmed to 3,500 feet of wire on each spool. The company ran the machine and then measured how much wire was actually on each spool. They found that the mean length was actually 3,510 feet and the standard deviation was 25 feet. They then ran the machine again and produced a sample of 400 spools of wire. Assume that the data is normally distributed.
1. Draw a normal distribution curve; be sure to include all the intervals and percentages.
2. What is the median and mode?
3. How many spools have at least 3,510 feet of wire?
4. How many spools have less than 3,485 feet of wire?
5. How many spools have between 3,485 and 3,560 feet of wire?
6. How many spools have between 3,460 and 3,535 feet of wire?
7. How many spools are within one standard deviation?
8. How many spools have less than 3,560 feet of wire?
9. How many spools make this inequality true: the amount of wire > 3,485 feet?
Click here to see answer by ikleyn(52781) |
Question 1204995: In a factory that produces wire, the spooling machine is programmed to 3,500 feet of wire on each spool. The company ran the machine and then measured how much wire was actually on each spool. They found that the mean length was actually 3,510 feet and the standard deviation was 25 feet. They then ran the machine again and produced a sample of 400 spools of wire. Assume that the data is normally distributed.
1. Draw a normal distribution curve; be sure to include all the intervals and percentages.
2. What is the median and mode?
3. How many spools have at least 3,510 feet of wire?
4. How many spools have less than 3,485 feet of wire?
5. How many spools have between 3,485 and 3,560 feet of wire?
6. How many spools have between 3,460 and 3,535 feet of wire?
7. How many spools are within one standard deviation?
8. How many spools have less than 3,560 feet of wire?
9. How many spools make this inequality true: the amount of wire > 3,485 feet?
Click here to see answer by Theo(13342)  |
Question 1202427: The average credit card debit for public school teacher is 14, 975. If the devt is normally distributed with a standard deviation of 650, find the probabilities (a) that the teacher owes at least 8, 740 (b) that the teacher owes more than 19, 270 (c) and that teacher owes between 6,740 and 19, 270
Click here to see answer by ikleyn(52781) |
Question 1194451: We have been using the normal distribution to approximate situations that are, in fact, binomial events. Create an example of a binomial event that can be approximated by a normal distribution and:
a)Demonstrate how accurate the approximation is by using both approaches to find the probability of the same event. Hint: Calculate the probability of the event as a binomial (sum of all binomial events) and calculate the probability of the approximated event using a normal distribution, and compare them to see how close the approximation is.
b)Describe the conditions under which the normal distribution would give a less accurate approximation.
Explain a situation in which the criteria for using the normal approximation would be met, i.e. np≥5 and n(1-p)≥5 , and yet you would decide not to use the normal distribution.
Click here to see answer by Boreal(15235)  |
Question 1194452: In many situations, the normal distribution can be used to approximate the binomial distribution.
a)Explain the conditions in which this can be done, and explain why we might take advantage of this property.
Click here to see answer by Boreal(15235) |
Question 1192857: In a normal distribution with mean 56 and standard deviation 21, how large a sample must be taken so that there will be at least a 90% percent chance that its mean is greater than
52? Recall that Z= x-mu/sigma/sqrt(n)
Can a tutor please assist me, what should I do to find n?
Click here to see answer by math_tutor2020(3817) |
Question 1192832: Kingston Electronics, inc., offers a “no hassle” returns policy. The number of items returned per day follows the normal distribution. The mean number of customer returns is 10.3 per day and the standard deviation is 2.25 per day.
1)The probability that the number of returns exceed a particular amount of 5%. What is the number of returns?
I did the following:
n= (z*std/Error)^2
(1.645* 2.25/.05)^2
Please assist me.
Click here to see answer by math_tutor2020(3817) |
Question 1192018: The scores in a Statistics test follow a normal distribution with an average score of 82 and standard deviation of 5. If all students who got 88 to 94 received a "very good", and it was announced that only 8 received a very good, how many students took the test?
Click here to see answer by Theo(13342) |
Question 1186734: The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.7 days and standard deviation of 1.8 days. Use your graphing calculator to answer the following questions. Write your answers in percent form. Round your answers to the nearest tenth of a percent.
a) What is the probability of spending less than 9 days in recovery? %
b) What is the probability of spending more than 4 days in recovery? %
c) What is the probability of spending between 4 days and 9 days in recovery? %
Click here to see answer by ikleyn(52781) |
Question 1186330: According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg (Kuulasmaa, Hense & Tolonen, 1998). Blood pressure is normally distributed.
a.) State the random variable.
b.) Suppose a sample of size 15 is taken. State the shape of the distribution of the sample mean.
c.) Suppose a sample of size 15 is taken. State the mean of the sample mean.
d.) Suppose a sample of size 15 is taken. State the standard deviation of the sample mean.
e.) Suppose a sample of size 15 is taken. Find the probability that the sample mean blood pressure is more than 135 mmHg.
f.) Would it be unusual to find a sample mean of 15 people in China of more than 135 mmHg? Why or why not?
g.) If you did find a sample mean for 15 people in China to be more than 135 mmHg, what might you conclude?
Click here to see answer by Boreal(15235) |
Question 1186173: Think of something in your work or personal life that you measure regularly (No actual calculation of the mean, standard deviation or z scores is necessary). What value is “average”? What values would you consider to be unusually high or unusually low? If a value were unusually high or low—how would it change your response to the measurement?
Click here to see answer by ikleyn(52781) |
Question 1186175: 1.) The commuter trains on the Red Line for the Regional Transit Authority (RTA) in Cleveland, OH,
have a waiting time during peak rush hour periods of eight minutes ("2012 annual report," 2012).
a.) State the random variable.
b.) Find the height of this uniform distribution.
c.) Find the probability of waiting between four and five minutes.
d.) Find the probability of waiting between three and eight minutes.
e.) Find the probability of waiting five minutes exactly.
Click here to see answer by greenestamps(13200)  |
Question 1186175: 1.) The commuter trains on the Red Line for the Regional Transit Authority (RTA) in Cleveland, OH,
have a waiting time during peak rush hour periods of eight minutes ("2012 annual report," 2012).
a.) State the random variable.
b.) Find the height of this uniform distribution.
c.) Find the probability of waiting between four and five minutes.
d.) Find the probability of waiting between three and eight minutes.
e.) Find the probability of waiting five minutes exactly.
Click here to see answer by ikleyn(52781) |
Question 1184185: Suppose that the mean retail price per gallon of regular grade gasoline in the United States is $3.45 with a standard deviation of $.20 and that the retail price per gallon has a bell shaped distribution. What percentage of a regular grade gasoline sold for more than $3.85 per gallon
Click here to see answer by Theo(13342) |
Question 1183503: . Public health records indicate that t weeks after the outbreak of a certain strain of influenza, approximately
Q(t) = 20
1 + 19 e−1.2t
thousand people had caught the disease.
(a) How many people had the disease when it broke out? How many had it 2 weeks later?
(b) At what time does the rate of infection begin to decline?
(c) If the trend continues, approximately how many people will eventually contract the disease? 7,343 people had
contracted the disease by the second week. (b) = t=2.454, so the epidemic begins to fade about 2.5 weeks after
it starts. (c) Q(t) approaches 20 as t increases without bound, it follows that approximately 20,000 people will
eventually contract the disease.
Click here to see answer by Solver92311(821)  |
Question 1182256: The red blood cell counts (in millions of cells per microliter) for a population of adult males can be approximated by a normal distribution, with a mean of 5.9 million cells per microliter and a standard deviation of 0.4 million cells per microliter.
(a) What is the minimum red blood cell count that can be in the top 23% of counts?
(b) What is the maximum red blood cell count that can be in the bottom 14% of counts?
(a) The minimum red blood cell count is________
nothing million cells per microliter?
(Round to two decimal places as needed.)
Click here to see answer by Boreal(15235) |
Question 1171969: A psychologist finds that the intelligence quotients of a group of patients are
normally distributed, with a mean of 102 and a standard deviation of 16. Find
the percent of the patients with IQs
a) above 114.
b) between 90 and 118.
Click here to see answer by VFBundy(438)  |
Question 1168799: Consider a normal distribution curve where 70-th percentile is at 15 and the 15-th percentile is at 1. Use this information to find the mean, 𝜇 , and the standard deviation, 𝜎 , of the distribution.( i don't know where or how to start this i am soooooooooooo lost
a) 𝜇=
b) 𝜎=
Click here to see answer by Boreal(15235) |
Question 1162941: Determine the following percentages for a z score of 0.90 (Round your answers to 2 decimal places
a. The percentage of scores fall below this z score.
b. The percentage of scores fall between the mean and this z score.
c. The percentage of scores above this z score
Click here to see answer by Theo(13342) |
Question 1159795: Test scores are normally distributed with a mean of 76 and a standard deviation of 10.
a. In a group of 230 tests, how many students score above 96?
b. In a group of 230 tests, how many students score below 66?
c. In a group of 230 tests, how many students score within one standard deviation of the mean?
Click here to see answer by Edwin McCravy(20055)  |
Question 1158686: A class is given an exam. The distribution of the scores is normal. The mean score is 80 and the standard deviation is 7. Determine the test score, c, such that the probability of a student having a score less than c is 90 %.
P(x < c) = 0.9
Find c rounded to one decimal place.
Click here to see answer by Boreal(15235) |
Question 1155349: Fuel economy estimates for automobiles built in a certain year predicted a mean of 26.2 mpg and a standard deviation of 5.8 mpg for highway driving. Assume that a normal distribution can be applied. Within what range are 95% of the automobiles?
Click here to see answer by Theo(13342) |
Question 1073285: the weight of a shipment of canned food are normally distributed. if 0.15% of them are lighter than 347 g and 2.5% of them are heavier than 377 g, find mean and the standard deviation of the weights of the canned food
Click here to see answer by Boreal(15235) |
Question 1073285: the weight of a shipment of canned food are normally distributed. if 0.15% of them are lighter than 347 g and 2.5% of them are heavier than 377 g, find mean and the standard deviation of the weights of the canned food
Click here to see answer by Theo(13342) |
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