Question

In: Statistics and Probability

A population of 1,000 students spends an average of $10.50 a day on dinner.

A population of 1,000 students spends an average of $10.50 a day on dinner. The standard deviation of the expenditure is $3. A simple random sample of 64 students is taken.

a. What are the expected value, standard deviation, and shape of the sampling distribution of the sample mean? Explain the reason. Which theorem ensures the shape of the sampling distribution?

b. What is the probability that these 64 students will spend a combined total of more than $715.21?

c. What is the probability that these 64 students will spend a combined total between $703.59 and $728.45?

 

Solutions

Expert Solution


Related Solutions

2. A population of 1,000 students spends an average of $10.50 a day on dinner. The...
2. A population of 1,000 students spends an average of $10.50 a day on dinner. The standard deviation of the expenditure is $3. A simple random sample of 64 students is taken. a. What are the expected value, standard deviation, and shape of the sampling distribution of the sample mean? b. Confirm that the Central Limit Theorem condition(s) have been met and draw the sampling distribution c. What is the probability that these 64 students will spend a combined total...
A population of 1,000 students spends an average of $10.50 a day on dinner. The standard...
A population of 1,000 students spends an average of $10.50 a day on dinner. The standard deviation of the expenditure is $3. A simple random sample of 64 students is taken. a. What are the expected value, standard deviation, and shape of the sampling distribution of the sample mean? b. What is the probability that these 64 students will spend an average of more than $11 per person? c. What is the probability that these 64 students will spend an...
Use the following information to answer questions 1-3. A population of 1,000 students spends an average...
Use the following information to answer questions 1-3. A population of 1,000 students spends an average of $10.50 a day on dinner. The standard deviation of the expenditure is $3. A simple random sample of 64 students is taken. Determine the expected value of the sample mean. a. $3.00 b. $10.50 c. $5.25 Determine the standard deviation of the sample mean. a. 0.363 b. 3.000 c. 0.375 Determine the probability that these 64 students will spend a combined total of...
The population of all Harvard students spends an average of $330 per semester on books. The...
The population of all Harvard students spends an average of $330 per semester on books. The population standard deviation of this expenditure is $65. A simple random sample of 40 students who attend the college is taken. a. Provide the sampling distribution for the sample mean. Can you assume a normal distribution for the sample mean? Why or why not? b. Calculate the probability that the average expenditure for the 40 students in the sample is between $320 and $350....
A typical college student spends an average of 2.55 hours a day using a computer. A...
A typical college student spends an average of 2.55 hours a day using a computer. A sample of 13 students at The University of Findlay revealed the sample mean of 2.70 hours and sample standard deviation of 0.51 hours. Can we conclude that the mean number of hours per day using the computer by students at The University of Findlay is the same as the typical student’s usage? Use the five step hypothesis testing procedure and the 0.05 significance level.
A survey of college students reported that they spend an average of $9.50 a day on...
A survey of college students reported that they spend an average of $9.50 a day on dinner with a standard deviation of $3. What is the probability that 100 randomly selected college students will spend less than $10.00 on average for dinner? Round your answer to 4 decimal places.
According to one study, an average student spends 4.4 hours on leisure activities per day. Assuming...
According to one study, an average student spends 4.4 hours on leisure activities per day. Assuming that the standard deviation of leisure activities per day is .5 hour. You took a sample of 16 students. Calculate the following: a. What is the probability that sample mean of leisure activities per day is more than 4.5 hours? b. Sample mean of leisure activities per day lies between 4.6 and 4.9 hours? c. Sample mean of leisure activities per day is less...
Students of a large university spend an average of $5 a day on lunch. The standard...
Students of a large university spend an average of $5 a day on lunch. The standard deviation of the expenditure is $3. A simple random sample of 36 students is taken. What are the expected value, standard deviation, and shape of the sampling distribution of the sample mean? What is the probability that the sample mean will be at least $4? What is the probability that the sample mean will be at least $5.90?
Students of a large university spend an average of $6 a day on lunch. The standard...
Students of a large university spend an average of $6 a day on lunch. The standard deviation of the expenditure is $2. A simple random sample of 81 students is taken. 1. What is the probability that the sample mean will be at least $5.25? 2. What is the probability that the sample mean will be at least $6.50? 3. What is the range of money spent by people who fall within one standard deviation of the mean? 4. Kelsey...
Students of a large university spend an average of $7 a day on lunch. The standard...
Students of a large university spend an average of $7 a day on lunch. The standard deviation of the expenditure is $2. A simple random sample of 25 students is taken. What is the probability that the sample mean will be at least $4? Jason spent $15 on his lunch. Explain, in terms of standard deviation, why his expenditure is not usual. Explain what information is given on a z table. For example, if a student calculated a z value...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT