Tutors Answer Your Questions about Probability-and-statistics (FREE)
Question 192905: A train traveling 50 mph left a station 30 minutes before a second train running at 55 mph. How soon did the second train overtake the first?
If 50x represents the distance the slower train travels, then the faster train travels
Click here to see answer by stanbon(75887)  |
Question 192977: Can people really identify their favorite brand of cola? Volunteers tasted Coca-Cola Classic, Pepsi, Diet Coke, and Diet Pepsi, with the results shown below. Research question: At α = .05, is the correctness of the prediction different for the two types of cola drinkers? Could you identify your favorite brand in this kind of test? Since it is a 2 × 2 table, try also a two-tailed two-sample z test for π1 = π2 (see Chapter 10) and verify that z2 is the same as your chi-square statistic.Which
test do you prefer? Why?
Correct? Regular Cola Diet Cola Row Total
Yes got it right 7 7 14
No got it wrong 12 20 32
Col Total 19 27 46
Click here to see answer by stanbon(75887) |
Question 193134: 4.) Nationwide, the average salary of actuaries who achieve that rank of Fellow is $150,000. An insurance executive wants to see how this compares with Fellows within his company. He checks the salaries of eight Fellows and find the average salary to be $155,500 with a standard deviation of $15,000. Can he conclude that fellows in his company make more than the national average, using standar deviation=0.05?
Thanks
Click here to see answer by stanbon(75887) |
Question 193188: The number of accidents per week at a hazardous intersection varies with mean 2.2 and standard deviation 1.4 accidents. This variable is discrete. It is certainly not normaly distributed. Let x-bar be the mean number of accidents per week at the intersection during a year.(52 weeks).
Question: What is the approximate chance that there are fewer than 130 accidents at the intersection a year? (Restate in terms of x-bar)
Click here to see answer by stanbon(75887) |
Question 193171: In a ten-question multiple-choice test with four choices for each question, a student who was not prepared guesses on each item. Find each probability.
a. P(six questions correct)
b. P(at least eight questions are correct)
c. P(fewer than eight questions correct)
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Question 193168: The breaking strengths of cables produced by a certain company are approximately normally distributed. The company announced that the mean breaking strength is 220 pounds. with a standard deviation of 188. A consumer protection agency claims that the actual standard deviation is higher. Suppose that the consumer agency wants to carry out a hypothesis test to see if its claim can be supported. State the null hypothesis Ho and the alternative hypothesis H1 they would use for this test.
Ho:
H1:
Click here to see answer by stanbon(75887) |
Question 192706: 2) Among a department's 16 trucks, 5 emit excessive amount of smoke. If 8 of the trucks are randomly selected for inspection, what with that this sample will include none of the trucks which emit excessive amount of smoke.?
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Question 192705: 1)Amoung 18 members of a cricket club, there are 2 wicket keepers, 5 bowlers and 6 batsman and 5 allrounders. What is the probability that a randomly selected team of 12 players comprise of 1 wicketkeeper, 3 bowlers, 4 batsman and remaining allrounders
Click here to see answer by stanbon(75887) |
Question 192817: Parametric and Nonparametric Data Identification Assignment
Label each of the following situations “P” if it is an example of parametric data or “NP” if it is an example of nonparametric data.
1. A manufacturer produces a batch of memory chips (RAM) and measures the mean-time-between-failures (MTBF). The manufacturer then changes a manufacturing process and produces another batch and again measures the MTBF. Did the change to the process improve the MTBF? __np__
2. From a written survey where the respondents were asked to rate an individual on a scale of 1 to 5, one group rated an individual a 3.7, another group rated the individual a 4.3. Is the difference statistically significant? ___p_
3. A catering company is buying equipment in order to set up their own store. They have a choice of two ovens that they can purchase for the store. The used oven is $100 less than the new oven, but its heating calibration is off by 20 degrees. Which one is a better buy for them? __np__
4. Jim Smith owns three real estate offices in Anytown. He has decided to open one more office, but he cannot decide between Hometown or Uptown as the town where he wants to locate. He will be comparing the mean number of homes sold per real estate agent, and the mean commission percentage earned by agents in the two towns to make his decision. _p___
5. A study to determine if job absenteeism is distributed evenly over the week. np____p
6. Mel’s Diner has been surveying their customers for the past couple of years about their dining experience in the restaurant. The survey uses a scale of one to five, five being best to indicate customer satisfaction. Mel’s customer satisfaction averaged 2.5 last year, but this year it is 2.9. Is this difference statistically significant? ___p_
7. Sally’s Beauty Salon just opened for business. Sally assigns the stylists customers on a rotation basis so that everyone is kept busy all day. One month after she opened the salon, Sally’s customer count for each stylist was (a) 20 customers; (b) 30 customers; (c) 15 customers; and (d) 25 customers. Has Sally been fair in how she allocates customers to each of the stylists? _p___
8. A comparison of salaries between male and female employees in the same organization. __p__
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Question 193296: 1) Two cards are drawn at random from a well shuffled pack of 52 cards. Find the probability that:
i) One is king and other is Queen.
ii) Both are of the same colour.
iii) Both are of the different colour.
Click here to see answer by Mathtut(3670) |
Question 193298: 3) An integer is chosen at random from the first 50bdigits. What is the probability that it is divisible by 6 or 8.
4) An integer is chosen at random from the first 100 positive integers. Find the probability that it is divisible by
i) 8 and 12.
ii) 16 and 20.
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Question 193299: Assume that 'x' is a number chosen at random from the sets of integers between 1 and 15 inclusive, what is the probability that 'x' is a:
i) Single digit number
ii) Multiple of 5 or 7
iii) Complete square.
Click here to see answer by Mathtut(3670) |
Question 193344: In the following regression, X = weekly pay, Y = income tax withheld, and n = 35 McDonald’s
employees. (a) Write the fitted regression equation. (b) State the degrees of freedom for a twotailed
test for zero slope, and use Appendix D to find the critical value at α = .05. (c) What is your
conclusion about the slope? (d) Interpret the 95 percent confidence limits for the slope. (e) Verify
that F = t2 for the slope. (f) In your own words, describe the fit of this regression.
R2 0.202
Std. Error 6.816
n 35
ANOVA table
Source SS df MS F p-value
Regression 387.6959 1 387.6959 8.35 .0068
Residual 1,533.0614 33 46.4564
Total 1,920.7573 34
Regression output confidence interval
variables coefficients std. error t (df = 33) p-value 95% lower 95% upper
Intercept 30.7963 6.4078 4.806 .0000 17.7595 43.8331
Slope 0.0343 0.0119 2.889 .0068 0.0101 0.0584
Click here to see answer by stanbon(75887) |
Question 193297: 2) A bag contains 9 white and 12 black balls. Find the probability of drawing 5 black balls.
3)A bag contains 2 red, 3 green, 5 blue, and 2 yellow balls. Find the probability that balls of all the colours are represented in a sample if four balls are selected at random.
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Question 193283: 19.) A biologist knows that the average length of a leaf of a certain full-grown plat is 4 inches. The standard deviation of the population is 0.6 inch. A sample of 20 leaves of that type of plant given a new type of plant food had an average lenght of 4.2 inches. Is there reason to believe that the new food is responsible for a change in the growth of the leaves? use α=0.01. Find the 99% confidence interval of the mean. DO the results occur? Explain. Assume that the variable is approximately normally distributed.
My answer, Ho:µ = 4 and H1:µ ≠4: C.V.= ±2.58
z=1.49; 3.85<µ<4.55; do not reject. There is not enough evidence to support the cail that the growth has change. Is this correct?
10.) The tennis Industry Association reported that 14% of tennis fans were female. If, in a sample of 30 tennis fans, 15 were female, do the results suggest that the percetage may have changed? use α = 0.02.
Please help me with this problems. Thanks.
Click here to see answer by stanbon(75887) |
Question 192692: The mean weight of adult mountain lions is 150lbs with a standard deviation of 8 lbs. A random sample of 50 mountain lions is selected.
a) What is the probability that the mean weight of the sample is less that 150 lbs?
b) What is the probability that the mean weight of the sample is between 149 and 151 lbs?
c) What is the probability that the mean weight of the sample is more than 153lbs?
What is the standard deviation of the sampling distribution?
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Question 193389: At a certain university, the average cost of books per student was $330 per student last semester. In a sample of 50 students this semester, their average cost was $355 with a standard deviation of $85. The Dean of Students believes that the costs are greater this semester. What is the test value for this hypothesis?
Click here to see answer by yuendatlo(23) |
Question 193386: An average computer mouse inspector can inspect 50 mice per hour. The 48 computer mice inspectors at a particular factory can only inspect 46 mice per hour with a standard deviation of 10. At = 0.025, does the company have reason to believe that these inspectors are slower than average?
Click here to see answer by yuendatlo(23) |
Question 193471: 2)In a group of 20 adults, 4 out of 7 women and 2out of 13 men wear glasses. What is the probability that a person chosen at random from the group is a women or someone who wear glasses.
3) A firm of charted accountants has two vacancies for trainee students. In the past , 40% of the students who were offered the training contract have not reported to join.If two students are offered training contract, what is the probability that one will join?
Click here to see answer by stanbon(75887) |
Question 193473: 4) An investment counselor claims that a stock price will go up is 0.60, remaining unchanged 0.37 or go down is 0.25. Explain what is wrong with the afore-stated statement.
5) Two cards are drawn in succession from a well shuffled pack of 52 playing cards. What is the probability that both drawn cards are Ace when
i) first drawn cards is replaced before the next draw, and
ii) first drawn cards is not replaced before the next draw? Mr.Stans Thanxs a lot this is my last question.
Click here to see answer by Mathtut(3670) |
Question 193546: Determining null and alternative hypotheses
A presidential candidate claims that the proportion of college students who are registered to vote in the upcoming election is at least 63%. Suppose that we want to sample a number of college students and carry out a hypothesis test to see if this claim may be refuted. State the null hypothesis Ho and the alternative hypothesis H1 that we would use for this test.
Ho:
H1:
Click here to see answer by stanbon(75887) |
Question 193574: Determining null and alternative hypotheses
The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.7 auto accidents per day with a variance of 0.0036 . The actuaries of the company claim that the variance of the number of accidents per day is no longer equal to 0.0036. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis Ho and the alternative hypothesis H1 that we would use for this test.
Ho:
H1:
Click here to see answer by stanbon(75887) |
Question 193513: The data given below are the final exam scores of 10 randomly selected statistics student and the number of hours they studied for the exam.
Subject # - 1 2 3 4 5 6 7 8 9 10
Hours, x - 6 8 5 11 5 7 7 8 9 6
Scores, y - 72 87 67 95 73 85 92 97 97 78
Part 1 : Find the mean hours of the 10 randomly selected students. Show the formula that you will use and then calculate the mean age.
Answer: Formula:
Mean:
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Question 193657: The lifetime of a certain brand of battery is known to have a standard deviation of 10.5 hours. Suppose that a random sample of 120 such batteries has a mean lifetime of 40.9 hours. Based on this sample, find the 95% confidence interval for the true mean lifetime of all batteries of this brand.
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Question 193656: In 1992, the FAA conducted 94,575 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 2,145 were positive.
(a) Construct a 99 percent confidence interval for the population proportion of positive drug tests.
(b) Why is the normality assumption not a problem, despite the very small value of the observed proportion (p)
Click here to see answer by stanbon(75887) |
Question 193654: A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were
3.28
3.25
3.25
3.3
3.33
3.36
3.07
3.29
3.47
3.4
(a)Construct a 95 percent confidence interval for the true mean weight.
(b) What sample size would be necessary to estimate the true weight with an error of ± 0.02 grams with 95 percent confidence?
(c) What factors might cause variation in the weight of Tootsie Rolls during manufacture?
Click here to see answer by stanbon(75887) |
Question 193851: From experience, a toll take on the Tri-State knows that the probability that an automobile paying a toll at the O’Hare Plaza is a Toyota is .21, that is a Honda is .17, and that is a Ford is .11. If one automobile pulls up to pay a toll, what is the probability that it is:
a) Toyota or a Honda?
b) None of the three makes?
Click here to see answer by edjones(8007)  |
Question 193875: In a survey of 212 people at the local track and field championship, 72% favored the home team winning. Find the margin of error for the survey, and give and interval that is likely to contain the exact percent of all people who favor the home team winning.
I got the Margin of Error: 6.86% but I have no idea on how to get the interval.
Thanks
Click here to see answer by stanbon(75887) |
Question 193844: A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were
3.28
3.25
3.25
3.3
3.33
3.36
3.07
3.29
3.47
3.4
(a) Construct a 95 percent confidence interval for the true mean weight.
(b) What sample size would be necessary to estimate the true weight with an error of ± 0.02 grams with 95 percent confidence?
(c) What factors might cause variation in the weight of Tootsie Rolls during manufacture?
Click here to see answer by stanbon(75887) |
Question 193969: It is claimed that the proportion of high school students in the United States who use computers for educational purposes is at most 70%. Suppose that we have reason to believe otherwise and wish to carry out a hypothesis test for this claim. State the null hypothesis Ho and the alternative hypothesis H1 that we would use for this test.
Ho:
H1:
Click here to see answer by stanbon(75887) |
Question 193951: A decade-old study found that the proportion of high school seniors who felt that "getting rich" was an important personal goal was 74%. Suppose that we have reason to believe that this proportion has changed, and we wish to carry out a hypothesis test to see if our belief can be supported. State the null hypothesis Ho and the alternative hypothesis H1 that we would use for this test.
Ho:
H1:
Click here to see answer by stanbon(75887) |
Question 193909: Sam is a representative who sells large appliances such as refrigerators, stoves, and so forth.Let x= number of appliances sam sells on a given day.Let F =frequency (number of days) with which he sells X appliances for a random sample of 240 days, Sam had the following sales record.
x|0|1|2|3|4|5|6|7
f|9|72|63|41|28|14|8|5
assume the sales record is representative of the population of all sales day.
A) use the relative frequency to find P(x) for x=0 to 7.
B)compute the probability that x is between 2 and 5 (including 2 and 5)
Click here to see answer by stanbon(75887) |
Question 194043: Sam is a representative who sells large appliances such as refrigerators, stoves, and so forth.Let x= number of appliances sam sells on a given day.Let F =frequency (number of days) with which he sells X appliances for a random sample of 240 days, Sam had the following sales record.
x|0|1|2|3|4|5|6|7
f|9|72|63|41|28|14|8|5
assume the sales record is representative of the population of all sales day.
d)compute the probability that x is less than 3.
e)compute the expected value of the x distribution.
f)compute the standard deviation of the x distribution.
Click here to see answer by stanbon(75887) |
Question 194063: My company has a fleet of 700 buses and 140 rail cars for urban mass transit
We repair everything ourselves. Recently we decided to try a Lean Manufacturing approach and try to optimize a standard engine rebuild that we do.
Our history data on the rebuild ( Same engine in all cases ) population mean was 34 hours with a 8 hour standard deviation.
After applying lean manufacturing principles on our rebuild team, we waited a few weeks for the "new" way to settle in then we retested to see if the times changed statistically
We sampled 30 jobs randomly and found a sample mean of 31 hours
Test at the 0.05 alpha, 2 tail test to see if we made statistical improvement 0.05 = 1.96
Click here to see answer by stanbon(75887) |
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