Question

In: Statistics and Probability

At a large university, the students have an average creditcarddebt of $2500,with a standard deviation of...

At a large university, the students have an average creditcarddebt of $2500,with a standard deviation of $1200. If we consider all of the possible random samples of 100students at this university, 95% of thesamples should have means between what two numbers? [HINT-use the 68-95-99.7Rule table in conjunction with the values for the sampling distribution model]

A)$100 and $2620

(B)$300 and $4900

(C)$2140 and $2860

(D)$2260 and $2740

Solutions

Expert Solution

Solution :

Given that,

= 2500

= 1200

= 100 and

= / n = 1200 / 100 = 1200 / 10 = 120

Using Empirical rule,

P( - 2< X < + 2) = 95%

P(2500 - 2 * 120 < X < 2500 * 2 * 120) = 95%

P(2260 < X < 2740) = 95%

D) $2260 and $2740


Related Solutions

A sample of university students has an average GPA of 2.78 with a standard deviation of...
A sample of university students has an average GPA of 2.78 with a standard deviation of 0.45. If GPA is normally distributed, what percentage of the students has GPAs….. More than 2.3? Less than 3.0? Between 2.00 and 2.5?
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...
Izmir Dokuz Eylul university students ' height is 168cm average and 10cm normal with standard deviation....
Izmir Dokuz Eylul university students ' height is 168cm average and 10cm normal with standard deviation. According to this, the height of a randomly selected student: a) be 165cm (5 points) B) 165 cm long to be long (5 points) c) 165 cm short (5 points) d) to be between 150cm and 160cm (10 points) Calculate their probability.
Students have an average GPA of 2.78 with a standard deviation of 0.45. You have been...
Students have an average GPA of 2.78 with a standard deviation of 0.45. You have been tasked by the university president to select a random sample of students, and to conduct in-depth interviews with them about how their academics were impacted by COVID-19. We would like the random students that you select to be representative of the entire student body, and therefore the GPA of your sample should be within 0.2 grade points of the population mean. How many students...
The average GPA at the University of North Carolina is 3.2, with a standard deviation of...
The average GPA at the University of North Carolina is 3.2, with a standard deviation of 0.3. Assume that all GPAs at the University of North Carolina are normally distributed. What is the probability of randomly selecting a student at the University of North Carolina with a GPA of 2.9 or lower? Possible answers: A. 0.10 B. 0.16 C. 0.24 D. 0.31 What is the probability of randomly selecting a student at the University of North Carolina with a GPA...
Professors at a local university earn an average salary of $80,000 with a standard deviation of...
Professors at a local university earn an average salary of $80,000 with a standard deviation of $6,000. The salary distribution is approximately bell-shaped. What can be said about the percentage of salaries that are less than $68,000 or more than $92,000? a. It is about 5%. b. It is about 32%. c. It is about 68%. d. It is about 95%.
A. The average SAT score of students is 1110, with a standard deviation ≈ 120. If...
A. The average SAT score of students is 1110, with a standard deviation ≈ 120. If a sample of n = 25 students is selected, what is the probability that the sample mean would be > 1150? That is, what is p(M>1150)? B. Which of the following will decrease statistical power? SELECT ALL THAT APPLY. a smaller sample size a larger effect size a larger standard deviation a larger alpha
The mean weight of students from a certain university is 70 kg with a standard deviation...
The mean weight of students from a certain university is 70 kg with a standard deviation of 17 kg. i. ii. iii. Assume that the weights of students in the university are normally distributed. What is the probability that the weight of a randomly chosen student is greater than 100 kg? What is the probability that the weight of a randomly chosen student is between 60 kg and 80 kg? If you were to take a sample of 16 students,...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT