Question

In: Statistics and Probability

According to an IRS study, it takes a mean of 400 minutes for taxpayers to prepare,...

According to an IRS study, it takes a mean of 400 minutes for taxpayers to prepare, copy and file a tax return. The standard deviation is 100 minutes. A consumer watchdog study select a random sample of 81 sample. What is the likelihood the sample mean is greater than 425 minutes?

Solutions

Expert Solution

SOLUTION:

From given data,

According to an IRS study, it takes a mean of 400 minutes for taxpayers to prepare, copy and file a tax return. The standard deviation is 100 minutes. A consumer watchdog study select a random sample of 81 sample.

The distribution of time follows the normal distribution with mean 400 and standard deviation 100.Random sample of 81 sample.

mean = = 400

standard deviation = = 100

sample size = n = 81

The standard error of the mean is,

= / sqrt(n)

= 100 / sqrt(81)

= 11.1111

= = 400

z = - / = - 400 / 11.1111

The standard error of the mean is 11.1111.

What is the likelihood the sample mean is greater than 425 minutes?

The likelihood the sample mean is greater than 425 minutes is,

P( > 425) = P((- ) / ​​​​​​​ > (425- 400) / 11.1111​​​​​​​)

P( > 425) = P(z > 2.25)

P( > 425) = 1 - P(z < 2.25)

P( > 425) = 1 - 0.98778 (FROM STANDARD NORMAL DISTRIBUTION TABLE)

P( > 425) = 0.01222

The likelihood the sample mean is greater than 425 minutes is 0.01222

orchestra answered 2 years ago
Next > < Previous

Related Solutions

Suppose taxpayers calling the IRS in 2017 waited 13 minutes on average for an IRS telephone assister to answer.
You may need to use the appropriate appendix table or technology to answer this question. Suppose taxpayers calling the IRS in 2017 waited 13 minutes on average for an IRS telephone assister to answer. Do callers who use the IRS help line early in the day have a shorter wait? Suppose a sample of 65 callers who placed their calls to the IRS in the first 30 minutes that the line is open during the day have a mean waiting...
5. The IRS reports that the mean refund for a particular group of taxpayers was $1,600....
5. The IRS reports that the mean refund for a particular group of taxpayers was $1,600. The distribution of tax refunds follows a normal distribution with a standard deviation of $850. a. What percentage of the refunds are between $1,600 and $2,000? b. What percentage of the refunds are between $900 and $2,000? c. What percentage of the refund are between $1,800 and $2,000? d. Ninety-five percent of the refunds are for less than what amount?
According to a national​ study, 38​% of taxpayers used computer software to do their taxes for...
According to a national​ study, 38​% of taxpayers used computer software to do their taxes for a certain tax year. A sample of 135 taxpayers was selected. Complete parts a through d below. a. Calculate the standard error of the proportion. ​(Round to four decimal places as​ needed.) b. What is the probability that less than 35​% of the taxpayers from the sample used computer software to do their​ taxes?​P(Less than 35​% of the taxpayers sampled used computer ​(Round to...
According to a national​ study, 38​% of taxpayers used computer software to do their taxes for...
According to a national​ study, 38​% of taxpayers used computer software to do their taxes for a certain tax year. A sample of 145 taxpayers was selected. Complete parts a through d below. a. Calculate the standard error of the proportion. sigma Subscript pequals nothing ​(Round to four decimal places as​ needed.) b. What is the probability that less than 34​% of the taxpayers from the sample used computer software to do their​ taxes? ​P(Less than 34​% of the taxpayers...
According to the IRS: "An IRS Audit is a review of an organizations or individuals accounts...
According to the IRS: "An IRS Audit is a review of an organizations or individuals accounts and financial information. Another way to look at an audit is as a discussion and review of the individuals or businesss financial situation to ensure taxpayers are complying with the tax laws and reporting a substantially correct amount of tax." Please describe the IRS audit process.
The IRS offers taxpayers the choice of allowing the IRS to compute the amount of their tax refund. During the busy filing season
The IRS offers taxpayers the choice of allowing the IRS to compute the amount of their tax refund. During the busy filing season, the number of returns received at the Springfield Service Center that request this service follows a Poisson distribution with a mean of three per day. What is the probability that on a particular day:a. There are no requests?b. Exactly three requests appear?c. Five or more requests take place?d. There are no requests on two consecutive days?
The mean time it takes aspirin to relieve headache pain is known to be 30 minutes....
The mean time it takes aspirin to relieve headache pain is known to be 30 minutes. A drug company has developed a new drug that they claim provides relief in less time. Government scientists tested the new drug on a sample of 25 individuals with headaches. For this sample, the mean time to relief was 26 minutes. The population standard deviation for the new drug is known to be 7 minutes. A level of significance of .01 is to be...
The mean time it takes aspirin to relieve headache pain is known to be 30 minutes....
The mean time it takes aspirin to relieve headache pain is known to be 30 minutes. A drug company has developed a new drug that they claim provides relief in less time. Government scientists tested the new drug on a sample of 25 individuals with headaches. For this sample, the mean time to relief was 26 minutes. The population standard deviation for the new drug is known to be 7 minutes. A level of significance of .01 is to be...
Suppose the probability of an IRS audit is 2.9 percent for U.S. taxpayers who file form...
Suppose the probability of an IRS audit is 2.9 percent for U.S. taxpayers who file form 1040 and who earned $100,000 or more. (a) What are the odds that such a taxpayer will be audited? (Round your answers to the nearest whole number.)    Odds that a taxpayer will be audited            to (b) What are the odds against such a taxpayer being audited? (Round your answers to the nearest whole number.)    Odds against a taxpayer being audited  ...
An employee takes time of her trip from her home to office as normally distributed with a mean of 21 minutes and a standard deviation of 7 minutes.
  An employee takes time of her trip from her home to office as normally distributed with a mean of 21 minutes and a standard deviation of 7 minutes. What proportion of her trip takes between 25 and 29 minutes? Draw the graph also.   Find the probability that standard normal random variable takes on the given values. Show the required area on the graph.   Pz=2.5   Pz0-Pz<-1.96   P-1.05<z   P-∞<z<+      2 P0<z<1  
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT