word problems

[orangeb]

Here are a few more questions that I got wrong and need help figuring out if anyone could help.

Question 1: The length of time for students to complete the Statistics exam is normally distributed with mean 75 minutes and standard deviation 15 minutes. How much time should be allowed so that 90% of the students will finish the exam?

I had the answer as 90% can finish between 45min and 105 min. What is the correct answer and what steps are used to get it?

Question 2: A traffic survey revealed that the speeds of vehicles along a dangerous strectch of interstate follow a normal distribution with mean 50 mph and standard deviation 8 mph. What speed limit should be posted so that only 8% of all drivers monitored are guilty of speeding?

I had the answer as 55. What is correct and what steps are used?


Question 3: Bank officials claim that the average amount of money in savings accounts at all branches of the Commerce Bank is $7,500, with a standard deviation of $650. Many random samples of size 100 are taken. Find the mean of these samples and the standard error of the mean.

I had the mean of the samples as $7500. How do I figure out the standard error of the mean?


Question 4: A survey of 49 randomly selected banks in New York revealed that these banks required average down payments of 35% of the purchase price of the home from new home buyers; the standard deviation was 5%. Find a 95% confidence interval for the true population standard deviation.


Question 5: Three hundred of 450 drivers surveyed indicated that they would consider buying retread tires. Find a 95% confidence interval for the true proportion of all drivers who might buy retread tires.

My answer for this one was so off that the teacher just had question marks all over my work on the page. So clearly I wasn't even headed towards a correct answer.

[JohnM]

Questions 1 and 2 have been asked on this forum before:

Question 1 (http://www.talkstats.com/statistics/446-statistics.html?highlight=finish+exam)

Question 2 (http://www.talkstats.com/statistics/447-speeding-nd.html?highlight=speeding)

(3) std error of the mean = standard deviation/square root of the sample size

(4) use the chi-square distribution - an example is here (http://www.talkstats.com/examples/230-computing-confidence-intervals.html)

(5) p = 300/450 = 0.667
use the same example post as #4

[feldner]

Question 3: Bank officials claim that the average amount of money in savings accounts at all branches of the Commerce Bank is $7,500, with a standard deviation of $650. Many random samples of size 100 are taken. Find the mean of these samples and the standard error of the mean.

This question was taken from above. Is it just simply $7,500 for the mean and using the formula of the standard deviation (650) divided by the square root of the sample size (10) to give me 6.50? This seems way to simple compared to the majority of these problems. Am I misreading what the question is actually asking? Does the phrase "many random samples" have any bearing on using the number 100?? Usually it takes me hours to figure these out, so I am apprehensive. Thank you for any enlightenment.

[JohnM]

Yes, you are correct. The mean of the samples will equal the population mean (over the long run) and the standard error of the sample means is simply s / sqrt(n).