Question

Assume the commuting times of American workers follow a normal distribution with mean mu=23 minutes and...

Assume the commuting times of American workers follow a normal distribution with mean mu=23 minutes and standard deviation sigma=5 minutes. A random sample of 16 American workers is taken. What is the probability that the sample mean commuting time is greater than 25 minutes?

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

The commuting times of American workers follow a normal distribution with mean = 23 minutes, and standard deviation of 5 minutes.

A random sample of 16 American workers is taken.

We have to find the probability that the sample mean is greater than 25 minutes.

If X be the random variable denoting the sample mean of these 16 workers, then X follows normal distribution with mean 23 and standard deviation of 5/sqrt(16), ie. 1.25.

We have to find

Where, phi is the distribution function of the standard normal variate.

From the standard normal table this becomes

So, the probability that the sample mean commuting time is greater than 25 minutes, is 0.0548.

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
the average employee in ontario spends mu=24.0 minutes commuting to work each day. Assume that the...
the average employee in ontario spends mu=24.0 minutes commuting to work each day. Assume that the distribution of commute times is normal with a standard deviation of sigma=8.0 minutes. a)what proportion of ontario employees spend less than 25 minutes a day commuting? b)what is the probability of randomly selecting an employee who spends more than 20 minutes commuting each day? c) what proportion of employees spend between 11 and 15 minutes commuting? d)what is the 50th percentile in this distribution...
The average employee in the U.S.A. spends μ = 23 minutes commuting to work each day....
The average employee in the U.S.A. spends μ = 23 minutes commuting to work each day. Assume that the distribution of commute times is normal with a standard deviation of σ = 8 minutes. (a) What proportion of U.S. employees spend less than 15 minutes a day commuting? (b) What is the probability of randomly selecting an employee who spends more than 35 minutes commuting each day?
- Assume that the commuting time on a particular train is uniformly distributed between 66 and...
- Assume that the commuting time on a particular train is uniformly distributed between 66 and 86 minutes. a. State the formula for the probability distribution function of commuting time on a train. b. What is the probability that the commuting time will be less than 80 minutes? c. What is the probability that the commuting time will be between 74 and 82 minutes? d. What is the probability that the commuting time will be greater than 83 minutes? e....
9. The time for a certain male student to commute to SCSU is Normally Distributed with...
9. The time for a certain male student to commute to SCSU is Normally Distributed with mean 48.3 minutes and standard deviation of 7.1 minutes. A random sample of 25 commuting times is taken. Find the 80th percentile of the sample mean of the commuting times. 10. The time for a certain male student to commute to SCSU is Normally Distributed with mean 48.3 minutes and standard deviation of 7.1 minutes. A random sample of 25 commuting times is taken....
The lifetime of a certain battery follows a normal distribution with a mean 276 minutes and...
The lifetime of a certain battery follows a normal distribution with a mean 276 minutes and standard deviation 25 minutes. We took a random sample of 100 of these batteries. What is the probability that the sample mean of the lifetime will be less than 270 minutes?
Commuting ~ According to 2016 U.S. Census, the average commuting time of Michiganders is 24.4 minutes....
Commuting ~ According to 2016 U.S. Census, the average commuting time of Michiganders is 24.4 minutes. A random sample of 120 Michigan workers has a mean commuting time of 23.08 minutes and a standard deviation of 8.3 minutes. Note: Numbers are randomized in each instance of this question. Pay attention to the numbers in this question. A researcher wonders if the actual mean commuting time of Michiganders is less than the value reported in the 2016 Census. What is the...
The minutes to commute to work is exponentially distributed with a mean of 20 minutes. a....
The minutes to commute to work is exponentially distributed with a mean of 20 minutes. a. Find the m value. b. Find the standard deviation. c. Find the probability of commuting less than 10 minutes. ?(? < 10) d. Find the probability of commuting greater than 25 minutes? ?(? > 25) e. Find the probability of commuting between 15 and 22 minutes? ?(15 < ? < 22) f. Find the probability of commuting 5 minutes? ?(? = 5)
At a large track meet, times in the 100-meter race follow a normal distribution with mean...
At a large track meet, times in the 100-meter race follow a normal distribution with mean 11.23 seconds and standard deviation 0.46 seconds. Times in the 200-meter race follow a normal distribution with mean 20.85 seconds and standard deviation 0.87 seconds. One runner had a time of 10.67 seconds in the 100-meter race. What must his 200-meter race time be in order for him to be at the same probability as the 100-meter race?
For each of the following scenarios, state whether the normal distribution may be used and justify...
For each of the following scenarios, state whether the normal distribution may be used and justify your answer. If the normal distribution can't be used, state which distribution should be used instead. a. A random sample of size 15 is taken from a normal population with standard deviation 5. Find the probability that the sample mean is greater than 28. b. A random sample of size 15 is taken from a normal population with standard deviation 5. Find the probability...
A company services home air conditioners. It is known that times for service calls follow a...
A company services home air conditioners. It is known that times for service calls follow a normal distribution with a mean of 60 minutes and a standard deviation of 10 minutes. A random sample of eight service calls is taken. What is the probability that exactly two of them take more than 68.4 minutes? For calculation convenience, you may round probability results to the nearest thousandth (3 decimals).
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT