Statistics and Probability Answers

A machine produces cylindrical metal pieces. A sample of pieces is taken, and the diameter are found to be 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01 and 1.03 cm. Find the t-value for a 98% confidence interval for the diameters of the cylindrical metal pieces. Assume that the diameters are approximately normally distributed.

Suppose that in a day, the probability of a car agent’'s not closing any deal is 0.35. on the other hand, the probability that he/she can close one deal is 0.3; two deals, 0.25; and three deals, 0.1. find the agent’s expected number of closed deals in a day and determine the variance and standard deviation.

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.