Tutors Answer Your Questions about Probability-and-statistics (FREE)
Question 1204806: Suppose you have a sample of 5 people where X represents cookie consumption in the past week. The following X:(6,5,4,1,1). What is the mean of X? Standard deviation of X? What is the Standard Error of X? Calculate the 95% confidence interval for X. Calculate the 99% confidence interval for X. Interpret your findings
Click here to see answer by Boreal(15235)   |
Question 1205490: The amount of gas a local gas station sells is random. The following describes the distribution of gasoline sales in a given day. There is a probability of 0.18 that the gas station will sell 1100 gallons of gas; probability of 0.20 that the gas station will sell 1400 gallons of gas; probability of 0.34 that the gas station will sell 1600 gallons of gas. Otherwise, the station sells 2100 gallons of gas. What is the expected number of gallons the station sells in a day?
Click here to see answer by math_tutor2020(3816) |
Question 1205491: In the past, the value of houses a local realtor has sold is normally distributed with a mean of $256,000 with a standard deviation of $60,000. How much does a house have to sell for so that the house is in the bottom 20% of lowest selling houses for the realtor?
Click here to see answer by ikleyn(52752)  |
Question 1205488: In the past, the value of houses a local realtor has sold is normally distributed with a mean of $230,000 with a standard deviation of $65,000. What is the probability that the next house the realtor sells has a value over $350,000? Probability the next house the realtor sells has a value under $350,000?
Click here to see answer by ikleyn(52752) |
Question 1205489: Suppose that when a Honda dealership sells a Honda Accord, the profit the dealership makes is normally distributed with a mean of $1200 and standard deviation of $350. Suppose that over a 2 month period of time, the dealership sells 50 Honda Accords. What is the probability that the dealership averages at least $1300 profit per car over that period of time?
Click here to see answer by Theo(13342)  |
Question 1205485: 12. A random sample of n = 4 individuals is selected from a population with µ = 35, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M = 40.1 with SS = 48.
(a)How much difference is there between the mean for the treated sample and the mean for the original population? (Note: In a hypothesis test, this value forms the numerator of the statistic.)
(b)If there is no treatment effect, how much difference is expected between the sample mean and its population mean? That is, find the standard error for M. (Note: In a hypothesis test, this value is the denominator of the t statistic.)
(c)Based on the sample data, does the treatment have a significant effect? Use a two-tailed test with α = .05.
Click here to see answer by Theo(13342) |
Question 1205509: If you solve the question below, I'll be appreciated.
An exam consists of 42 multiple-choice questions. Each question has a choice of five answers, only one of which is correct. For each correct answer, a candidate gets 1 mark, and no penalty is applied for getting an incorrect answer. A particular candidate answers each question purely by guess-work.
Using Normal approximation to Binomial distribution with continuity correction, what is the estimated probability this student obtains a score greater than or equal to 10? Please use R to obtain probabilities and keep at least 6 decimal places in intermediate steps.
A. 0.6643
B. 0.2089
C. 0.4059
D. 0.3357
E. 0.5650
Click here to see answer by Theo(13342) |
Question 1205511: If you solve the question below, I'll be appreciated.
The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean \mu = 548.7 and standard deviation \sigma = 25.9.
(a) What is the probability that a single student randomly chosen from all those taking the test scores 555 or higher?
ANSWER: ?
For parts (b) through (d), consider a simple random sample (SRS) of 35 students who took the test.
(b) What are the mean and standard deviation of the sample mean score \bar x, of 35 students?
The mean of the sampling distribution for \bar x is: ?
The standard deviation of the sampling distribution for \bar x is: ?
(c) What z-score corresponds to the mean score \bar x of 555?
ANSWER: ?
(d) What is the probability that the mean score \bar x of these students is 555 or higher?
ANSWER: ?
Click here to see answer by Theo(13342) |
Question 1205508: If you solve the question below, I'll be appreciated.
A statistics practitioner took a random sample of 48 observations from a population whose standard deviation is 24 and computed the sample mean to be 98.
Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits.
A. Estimate the population mean with 95% confidence.
Confidence Interval = ?
B. Estimate the population mean with 95% confidence, changing the population standard deviation to 49;
Confidence Interval = ?
C. Estimate the population mean with 95% confidence, changing the population standard deviation to 6;
Confidence Interval = ?
Click here to see answer by Theo(13342) |
Question 1205518: If you solve the question below, I'll be appreciated.
The level of nitrogen oxides (NOX) in the exhaust of a particular car model varies with mean 0.9 grams per mile and standard deviation 0.2 grams per mile .
(a) What sample size is needed so that the standard deviation of the sampling distribution is 0.01 grams per mile ?
ANSWER: ?
(b) If a smaller sample is considered, the standard deviation for \bar x would be ? . (NOTE: Enter ''SMALLER'',''LARGER'' or ''THE SAME'' without the quotes.)
Click here to see answer by MathLover1(20849)  |
Question 1205517: If you solve the question below, I'll be appreciated.
A study on the length of time a person brushes their teeth is conducted on a large population of adults. The mean brushing time is \mu and the standard deviation is \sigma. A simple random sample of 270 adults is considered.
(NOTE: For the following problems enter: '' GREATER THAN '', '' EQUAL TO '', '' LESS THAN '', or '' NOT ENOUGH INFORMATION '', without the quotes.)
(a) The mean of the sampling distribution is ? the mean of the population.
(b) The standard deviation of the sampling distribution is ? the standard deviation of the population.
Click here to see answer by MathLover1(20849) |
Question 1205525: According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 67 inches and a standard deviation of 2.3 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(67,2.3)
b. Find the probability that the person is between 63.9 and 66.7 inches.
c. The middle 20% of Martian heights lie between what two numbers?
Low:
High:
Click here to see answer by ikleyn(52752) |
Question 1205516: If you solve the question below, I'll be appreciated.
An HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells you that the printing speed is actually a Normal random variable with a mean of 17.08 ppm and a standard deviation of 4.5 ppm. Suppose that you draw a random sample of 12 printers.
Part i) Using the information about the distribution of the printing speeds given by the manufacturer, find the probability that the mean printing speed of the sample is greater than 17.18 ppm. (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places).
Probability (as a proportion) ?
Part ii) Use normal approximation to find the probability that more than 44.9% of the sampled printers operate at the advertised speed (i.e. the printing speed is equal to or greater than 18 ppm)
A. 0.5070
B. 0.5834
C. 0.4930
D. 0.4166
Click here to see answer by Theo(13342) |
Question 1205548: Five students, A, B, C, D and E, are passing a ball, initially A holds the ball. If after 3 passes A holds the ball again and after 6 passes A holds the ball again, how many possible ways of passing the ball are there?
Click here to see answer by ikleyn(52752) |
Question 1205579: Question # 05
(i) A single die is rolled 4 times. Find the probability of getting at least one 5.
(ii) In a certain high-risk group, the chances of a person having suffered a heart attack are 55%. If 6 people are chosen, find the probability that at least 1 will have had a heart attack. (hint: Binomial Dist)
(Hi)
A box contains black chips and white chips. A person selects two chips without replacement. If the probability of selecting a black chip and a white chip is, and the probability of selecting a black chip on the first draw is i, find the probability of selecting the white chip on the second draw, given that the first chip selected was a black chip.
probability)
(hint: conditional
(iv)
A recent survey asked 100 people if they thought women in the armed forces should be permitted to participate in combat. The results of the survey are shown.
Gender
Yes
No
Total
Male
Female
32
18
50
50
Total
40
60
100
Find these probabilities.
a. The respondent answered yes, given that the respondent was a female.
b. The respondent was a male, given that the respondent answered no.
(v) (Hint: Independent events)
A coin is flipped and a die is rolled. Find the probability of getting a head on the coin and a 4 on the die.
(vi)
The corporate research and development centers for three local companies have the following number of employees:
U.S. Steel
Alcoa
110
Bayer Material Science
750
250
If a research employee is selected at random, find the probability that the employee is employed by U.S. Steel or Alcoa.
Click here to see answer by ikleyn(52752) |
Question 1205585: Mr. and Mrs. Doran have a genetic history such that the probability that a child being born to them with a certain trait is 4/5. If they have seven children, what is the probability that exactly one of their seven children will have that trait? Round your answer to the nearest thousandth.
Click here to see answer by ikleyn(52752) |
Question 1205590: Distance C was measured 7 times with one measuring device and 7 times with another measuring device. The measurement results (in meters) are as follows:
1. Measuring device 1: 200 201 200 200 199 200 200
2. Measuring device 2: 201 200 198 202 202 200 201
1) Test whether the variances can be considered equal with a probability of 0.95.
2) Test whether the measurement results differ significantly with a probability of 0.95.
Click here to see answer by Theo(13342) |
Question 1205588: The distance A was measured 14 times with the same measuring device. The measurement results (in meters) are as follows: 50, 51, 49, 48, 50, 50, 49, 49, 49, 50, 49, 50, 50, 54.
Create a variation line, calculate the sample mean, the standard deviation of the measurement, the coefficient of variation, and the sample mean relative standard error.
Click here to see answer by MathLover1(20849) |
Question 1205726: Two students agreed to meet at the Library between 6 pm and 7 pm. They also agree that the student arriving first will wait for a maximum of 25 minutes. What is the probability that they will meet, if they arrive at the Library between 6 pm and 7 pm randomly (uniform random distribution)?
Click here to see answer by ikleyn(52752) |
Question 1205726: Two students agreed to meet at the Library between 6 pm and 7 pm. They also agree that the student arriving first will wait for a maximum of 25 minutes. What is the probability that they will meet, if they arrive at the Library between 6 pm and 7 pm randomly (uniform random distribution)?
Click here to see answer by greenestamps(13195)  |
Question 1205739: A bag contains 10 red marbles, 9 white marbles, and 8 blue marbles. You draw 5 marbles out at random, without replacement. What is the probability that all the marbles are red?
The probability that all the marbles are red is .
What is the probability that exactly two of the marbles are red?
The probability that exactly two of the marbles are red is .
What is the probability that none of the marbles are red?
The probability of picking no red marbles is
Click here to see answer by greenestamps(13195) |
Question 1205760: A survey of an urban university showed that 865 of 1,360 students sampled supported a fee increase to fund improvements to the student recreation center. Using the 95% level of confidence, what is the confidence interval for the proportion of students supporting the fee increase?
Select one:
a. [0.559, 0.713]
b. [0.604, 0.668]
c. [0.610, 0.662]
d. [0.616, 0.656]
Click here to see answer by math_tutor2020(3816) |
Question 1205765: 27% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and ask each to name the reason he or she uses credit cards. Find the probability that the number of college students who say they use credit cards because of the rewards program is (a) exactly two, (b) more than two,
and (c) between two and five inclusive. If convenient, use technology to find the probabilities.
Click here to see answer by ikleyn(52752) |
Question 1205813: The average miles driven annually per licensed driver in the United States is approximately 14,090 miles. If we assume a fairly mound shaped distribution with a standard deviation of approximately 3500 miles, find the mileage that corresponds to a z-score equal to 2.14.
Click here to see answer by ikleyn(52752) |
Question 1205818: A distribution of measurements has a mean of 85 and a standard deviation of 3. You know nothing else about the size or shape of the data. Use this information to find the proportion of measurements in the given interval. (Round your answer to two decimal places.)
between 76 and 94
Click here to see answer by ikleyn(52752) |
Question 1205782: Each Filipino uses an average of 650 pounds of plastic in a year. Suppose that the distribution is approximately normal with a population standard deviation of 153.5 pounds. Assume the variable is normally distributed. Find the probability that a randomly selected Filipino uses
a.) More than 800 pounds of paper in a year (10 points)
b.) Less than 400 pounds a year (10 points)
c.) Between 500 and 700 pounds a year (10 points)
Click here to see answer by Theo(13342) |
Question 1205768: It is claimed that a random sample of 49 tyres has mean life of 15200 km. This sampled was drawn from a population whose mean is 15150 km's and a standard deviation of 1200 km. Test the significance at 0.05 level.
Click here to see answer by Theo(13342) |
Question 1205804: The weather forecast in the cities of a province is modelled using a simple model that determines whether it will rain, be cloudy or sunny, only by
taking into account the previous day's weather. In this case, the model tells us that:
- a sunny day has a 70% chance that it will still be sunny the following day
- a rainy day has a 70% chance that it will still be rainy the next day
- sunny days and rainy days cannot be consecutive
- the probability that a cloudy day remains cloudy coincides with the normalised distance from the city to a reference centre. This probability is
we denote byr
- finally, the probability that a cloudy day becomes rainy or sunny is the same.
1. Write the transition matrix A (as a function of the parameter r)
I did the transition matrix A. Please see below:
rainy [7/10, -1/2r + 1/2, 3/10]
A= cloudy[0, r, 0]
sunny [3/10, -1/2 + 1/2, 7/10]
According to the exercise the sum of the elements in each column must be 1.
I can't understand the next exercise, can somebody help me?
2. We know that in a city today is a cloudy day and that the forecast for tomorrow is: 17 % rainy, 66 % cloudy and 17 % sunny. What is the normalised distance from this city to the reference point?
i don't underestand how to do it.
Click here to see answer by ikleyn(52752) |
Question 1205866: A survey of a group's web habits for the past month obtained the following information.
30% visited Facebook.
38% visited LinkedIn.
36% visited Google.
16% visited Facebook and LinkedIn.
16% visited Facebook and Google.
18% visited LinkedIn and Google.
9% visited all three sites.
Find the percentage that visited none of these three sites last month.
Hint: Draw a Venn diagram for three sets. Then label appropriate parts from the given information.
Click here to see answer by ikleyn(52752) |
Question 1205900: The weights (in pounds) of 27 packages of ground beef in a supermarket meat display are as follows.
1.10 1.01 0.99 1.20 1.41 1.28 0.83
1.04 1.16 1.36 0.75 0.96 1.08 0.87
0.91 0.87 0.98 1.12 1.10 0.95 1.22
0.87 0.98 1.12 0.90 1.16 1.15
Find the percentage of measurements in the intervals
x ± s, x ± 2s, and x ± 3s. (Round your answers to the nearest percent.)
Click here to see answer by ikleyn(52752) |
Question 1205901: Breathing rates for humans can be as low as 4 breaths per minute or as high as 70 or 75 for a person doing strenuous exercise. Suppose that the resting breathing rates for college-age students have a distribution that is mound-shaped, with a mean of 14 and a standard deviation of 2.5 breaths per minute.
What fraction of all students would have breathing rates in the following intervals? more than 21.5 or less than 6.5 breaths per minute.
Click here to see answer by ikleyn(52752) |
Question 1205906: A random variable follows a binomial distribution with a probability of success equal to 0.57. For a sample size of n=12, find the values below.
a. the probability of exactly 3 successes
b. the probability of 7 or more successes
c. the probability of exactly 10 successes
d. the expected value of the random variable
Click here to see answer by ikleyn(52752) |
Question 1205905: A random variable follows a binomial distribution with a probability of success equal to 0.72. For a sample size of n=10, find the values below.
a. the probability of exactly 5 successes
b. the probability of 6 or more successes
c. the probability of exactly 9 successes
d. the expected value of the random variable
Click here to see answer by ikleyn(52752) |
Question 1205902: The mean percent of childhood asthma prevalence in 43 cities is 2.21%. A random sample of 34 of these cities is selected. What is the probability that the mean childhood asthma prevalence for the sample is greater than 2.4%? Interpret this probability. Assume that the standard deviation is 1.22%.
Click here to see answer by Theo(13342) |
Question 1205937: bag contains 44 U.S. quarters and six Canadian quarters. The coins are identical in size) If six quarters are randomly picked from the bag, what is the probability of getting at least one Canadian quarter? (Round your answer to one decimal place)
Click here to see answer by ikleyn(52752) |
Question 1205917: a teacher gives a test consisting of 10 questions with 2 possible answers. obviously the student can answer the guesses. to test the hypothesis that
the student just guesses:
a. if the student has 7 or more correct answers, he did not guess
b. if he has less than 7 correct answers, the student goes by guess or by chance
To determine the probability of rejecting the hypothesis that it is correct. To determine the probability of acceptance of the previous hypothesis when the probability
of correct answers to the question is 0.7
Click here to see answer by greenestamps(13195) |
Question 1205947: A consultant is beginning work on three projects. The expected profits from these projects are $41 thousand, $60 thousand, and $15 thousand respectively. The associated standard deviations are $13 thousand, $16 thousand, and $5 thousand respectively. Answer the following, rounding your answers to two decimal places.
(a) Assuming independence of outcomes, find the mean (in thousands of $) of the consultant's total profits from these three projects.
(b) Assuming independence of outcomes, find the standard deviation (in thousands of $) of the consultant's total profits from these three projects.
Click here to see answer by ikleyn(52752) |
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