Question

In: Statistics and Probability

Suppose the mean wait time for a bus is 30 minutes and the standard deviation is...

Suppose the mean wait time for a bus is 30 minutes and the standard deviation is 10 minutes. Take a sample of size n = 100.

Find the probability that the sample mean wait time is between 29 minutes and 31 minutes.

Solutions

Expert Solution

Solution :

Given that ,

mean =   = 30

standard deviation = = 10

n = 100

= 30

=  / n= 10 / 100= 1

P(29<     <31 ) = P[(29 - 30) /1 < ( - ) /   < (31 - 30) /1 )]

= P( -1< Z < 1)

= P(Z < 1) - P(Z < -1)

Using z table

=0.8413 - 0.1587

probability= 0.6826


Related Solutions

Suppose the mean wait time for a bus is 30 minutes and the standard deviation is...
Suppose the mean wait time for a bus is 30 minutes and the standard deviation is 10 minutes. Take a sample of size n = 100. Find the probability that the sample mean wait time is more than 31 minutes.
Suppose the mean wait time for a bus is 30 minutes and the standard deviation is...
Suppose the mean wait time for a bus is 30 minutes and the standard deviation is 10 minutes. Take a sample of size n = 100. Find the 95th percentile for the sample mean wait time.
The mean wait time at Social Security Offices is 25 minutes with a standard deviation of...
The mean wait time at Social Security Offices is 25 minutes with a standard deviation of 11 minutes. Use this information to answer the following questions: A.            If you randomly select 40 people what is the probability that their average wait time will be more than 27 minutes? B.            If you randomly select 75 people what is the probability that their average wait time will be between 23 and 26 minutes? C.            If you randomly select 100 people what is...
The mean wait time at Social Security Offices is 25 minutes with a standard deviation of...
The mean wait time at Social Security Offices is 25 minutes with a standard deviation of 11 minutes. Use this information to answer the following questions: A.            If you randomly select 40 people what is the probability that their average wait time will be more than 27 minutes? B.            If you randomly select 75 people what is the probability that their average wait time will be between 23 and 26 minutes? C.            If you randomly select 100 people what is...
1.            The mean wait time at Social Security Offices is 25 minutes with a standard deviation...
1.            The mean wait time at Social Security Offices is 25 minutes with a standard deviation of 11 minutes. Use this information to answer the following questions: A.            If you randomly select 40 people what is the probability that their average wait time will be more than 27 minutes? B.            If you randomly select 75 people what is the probability that their average wait time will be between 23 and 26 minutes? C.            If you randomly select 100 people what...
The amount of time, in minutes that a person must wait for a bus is uniformly...
The amount of time, in minutes that a person must wait for a bus is uniformly distributed between 4 and 16.5 minutes, X~U(4, 16.5). a.) Find the mean of this uniform distribution. b.) Find the standard deviation of this uniform distribution. c.) If there are 16 people waiting for the bus and using the central limit theorem, what is the probability that the average of 16 people waiting for the bus is less than 8 minutes? Please type detailed work...
Suppose the mean and the standard deviation of the waiting times of passengers at the bus...
Suppose the mean and the standard deviation of the waiting times of passengers at the bus station near the Cross Harbour Tunnel are 11.5 minutes and 2.2 minutes, respectively. (a) Assume the waiting times are normally distributed. How likely a randomly selected passenger waits less than 15 minutes at the bus station? (b) Assume the waiting times are normally distributed. 82% of the passengers at the bus station are expected to wait more than k minutes. Find k. (c) For...
The metropolitan bus company claims that the mean wait time for a bus during rush hour...
The metropolitan bus company claims that the mean wait time for a bus during rush hour is less than 7 minutes. A random sample of 20 waiting times has a mean of 5.6 minutes with a standard deviation of 2.1 minutes. At a= 0.01, test the bus company’s claim. Assume the distribution is normally distributed.
Suppose that an individual showing up to a bus stop must wait x minutes for a...
Suppose that an individual showing up to a bus stop must wait x minutes for a bus, where x follows a uniform distribution between 0 and 45 minutes. 1. What is the probability that someone will have to wait between 30 and 40 minutes for a bus? 2. If we took many random samples of 50 people waiting for the bus, the sampling distribution of the average wait time of these samples should be normal with a mean of _______...
Suppose the average length of a TTC delay is 30 minutes with a standard deviation of...
Suppose the average length of a TTC delay is 30 minutes with a standard deviation of 5.5 minutes. A local business estimates that the cost to their business associated with these delays 150H^2 −8.50, where H is the duration of a TTC delay in hours. How much will a TTC delay cost, at least 70% of the time? Show all your work and include any annotations you think would be helpful in explaining your process. You may find it helpful...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT