Statistics and Probability Answers

Five hundred tickets will be sold and these will be raffled during the town fiesta. One of these tickets will win Php 3,000 and the rest will win nothing. What will be the expected outcome and variance of your gain if you will buy one of the tickets?

1. In a learning style study, 1200 respondents were asked if they can assimilate concepts while watching television. 568 said Yes. Find a 95% confidence interval for the population p (Explain your solutions):
2. What is α?
3. What are the confidence coefficients?
4. what are p and q?
5. The error E is approximately?
6. What are the lower and upper limits?
7. The true population proportion falls between?

1. In a learning style study, 1200 respondents were asked if they can assimilate concepts while watching television. 568 said Yes. Find a 95% confidence interval for the population p (Explain your solutions):
2. What is α?
3. What are the confidence coefficients?
4. what are p and q?
5. The error E is approximately?
6. What are the lower and upper limits?
7. The true population proportion falls between?

A division-wide aptitude test in Mathematics was conducted to 1000 pupils. The mean of the test is 58 and the standard deviation is 12. The scores also approximate the normal distribution.

What is the minimum score to belong to the upper 10% of the group?

What are the two extreme scores outside of which 5% of the group and expected to fall?

What is the score that divides the distribution into two such that 75% of the cases is below it?

Estimate the range of scores that will include the:

Middle 50% of the distribution.

Middle 99% of the distribution.

   1. P( < 2.20)

     2. P( -2.5 < z < 2.01) 

The following data represent a random sample of 15 marks out of 20) on a Statistics quiz. Assume that the marks are normally distributed 4 7 7 5 3 10 6 8 7 9 8 9 5 4 7 a. Determine the standard deviation of the marks. b. Estimate the population mean with 95% confidence.

The number of accidents in a production facility has a Poisson distribution with a mean of 2.8 per month. For a given month, what is the probability that there will be more than three (3) accidents?

A researcher is interested in estimating the average monthly salary of bank managers in NCR. He wants to be 90% confident that his estimate is correct. If the standard deviation is 8,500 pesos, how large a sample is needed te get the desired information and to be accurate within 1,150 pesos?

A university conducted a tracer study to track its graduates for the past five years. One of the variables included in the study questionnaire asks for data on the monthly salaries of the graduates. A sample of 90 graduates yielded a sample mean equal to Php37 000. Construct a 90% confidence interval for the population mean monthly salary if it is known that the population standard deviation is Php9 470. Interpret the result (Write the interpretation in your solution).

A. 37,000 < μ < 39,000

B. 35,350.01 < μ < 38,640.08

C. 35,357.92 < μ < 38,642.08

D. 37,742.92 < μ < 39,875.01

Given a normal distribution with a mean of 200 and the deviation is10. Find the area above 188.