Math Answers

The sample space contains 6 As and 4 Bs. What is the probablity that a randomly selected set of 3 will include 2 As and 1 B​?

A. Find the length of the confidence interval (s = standard deviation)

1. s = 3

n = 250

Confidence level = 95%

2. s = 6

n = 400

Confidence level = 99%

B. Determine the sample size, given the following data.

1. s = 5

E = 2.42

Confidence level = 95%

2. You want to estimate the mean gasoline price within your town to the margin of error of 6 centavos. Local newspaper reports the standard deviation for gas price in the area is 30 centavos. What sample size is needed to estimate the mean gas prices at 99% confidence level?

3. Carlos wants to replicate a study where the highest observed value is 14.8 while the lowest is 14.2. He wants to estimate the population mean µ to the margin of error of 0.025 of its true value. Using 95% confidence level, find the sample size n that he need.

A. Find the length of the following confidence interval.

1. Upper limit = 0.995

Lower Limit = 0.437

2. Upper limit = 394.14

Lower Limit = 354.74

3. Upper limit = 0.02946

Lower Limit = 0.02244

4. 0.475 < p < 0.735

5. 0.355 < p < 0.570

A fruit juice franchise company has a policy of opening new fruit juice stand only on those areas that have a mean household income of at least ₱30,500 a month. The company is currently considering an area in which to open a new fruit juice stand. The company’s research department took a sample of 25 households from this area and found that the mean monthly income of these households is ₱32,600. Using 5% significance level, would you conclude that the company should open a fruit juice stand in the area? Also, find the 95% confidence interval of the true mean.

The treasurer of a municipality claims that the average net worth of families living in this municipality is ₱590,000. A random sample of 50 families selected from this area produced a mean net worth of ₱720,000 with standard deviation of ₱65,000. Using 1% significance level, can we conclude that the claim is true? Also, find the 99% confidence interval of the true mean.

6. Lilian got a score of 55, which is equivalent to the 70th percentile in a mathematics test. Which of the following is NOT true?

A. 70% of the students got a score less than or equal to Lilian’s score.

B. Thirty percent of the class got scores of 55 and above.

C. If the passing mark is the first quartile, she passed the test.

D. Her score is below the 5th decile.

7. In a 50-item test, Angela got a score of 35 which is the third quartile. This means that:

A. She got the highest score.

B. Her score is higher than 25% of her classmates.

C. She surpassed 75% of her classmates.

D. Seventy-five percent of the class did not pass the test.

8. In the set of scores 14, 17, 10, 22, 19, 24, 8, 12, and 19, the median score is _______. A. 17 C. 16 B. 15 D. 13

The weights of the students in a class are the following: 69, 70, 75, 66, 83, 88, 66, 63, 61, 68, 73, 57, 52, 58, and 57.

8. Find the value of D8 of the students’ weights.

9. Calculate the value of D4 of the students’ weights.

10. What is the Q2 of the students’ weights?

The scores of Miss San Quintin candidates from seven judges were recorded as follows: 8.12, 9.10, 8.42, 9.14, 8.75, 9.17, and 8. 37 

For numbers 4 – 6, refer to the given data above.

4. Find the 50th percentile or P50 of the judges’ scores.

5. What is the P30 of the judges’ scores? 

6. Determine the 70th percentile of the judges’ scores

7. Calculate P40 of the judges’ scores

Between z = – 2.39 and z = – 1.05  

On an average 5% of the population in an area suffers from Diabetes. What is the probability that out of 7 persons chosen at random from this area with less than and equals to three suffer from the disease