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Consider the following relations on {1, 2, 3, 4}.
R1 = {(2,2), (2,3),(2,4),(3,2),(3,3),(3,4)}
R2 = {(1,1),(1,2),(2,1),(2,2),(3,3),(4,4)}
R3 = {2,4),(4,2)}
R4 = {(1,2),(2,3),(3,4)}
R5 = {(1,1),(2,2),(3,3),(4,4)}
a) Which of these relations are reflexive? Justify your answers.
b) Which of these relations are symmetric? Justify your answers.
c) Which of these relations are antisymmetric? Justify your answer.
d) Which of these relations are transitive? Justify your answers.
the average grade of senior high school students in general mathematics is 89 and the standard deviation is 2.5 assume that the variable ks normally distributed.
a. what is the probability that the grades is will be larger than 92 if a grade selected?
b. if a sample of 15 grades is selected, what is the probability that the mean of the sample will be greater than 92?
the allowance of junior high school students is normally distributed has a mean of 18.3 pesos and standard deviation of 1.5 pesos. if 60 samples consisting og 13 JHS each are drawn from the population,what is the mean and standard deviation of the sampling distribution of means? assume that the population is infinite.
Find the linear and Bernoulli’s differential equations from the following differential equations and solve it.
i) (1 − 𝗑2) 𝑑𝑦 − 𝗑𝑦 = 1.
ii) 𝑑𝑦/dx = 𝗑𝑦2 − 𝗑𝑦.
Clarendon College claims that some of their BSEd first year students shifted to another course because of their retention policy, which is normally distributed. A random sample of 200 students revealed that 55 of them shifted to another course after their first year.
1. Compute the proportion estimate of the parameter.
2. Compute the standard error of the proportion.
3. Compute the margin of error of the proportion at 90% confidence level.
4. Find 95% confidence interval for all the BSED students shifted to another course after their first year because of the retention policy.
Clarendon College claims that some of their BSEd first year students shifted to another course because of their retention policy, which is normally distributed. A random sample of 200 students revealed that 55 of them shifted to another course after their first year.
1. Compute the proportion estimate of the parameter.
2. Compute the standard error of the proportion.
3. Compute the margin of error of the proportion at 90% confidence level.
4. Find 95% confidence interval for all the female employees in the government agencies holding executive positions.
Based from the results of a survey conducted by a group of researchers, the proportion of feinales holding executive positions in the government agencies in a certain populated city in the Philippines is normally distributed, in a random sample of 300 female employees in government agencies, 75 female employees hold executive positions.
1. Compute the proportion estimate of the parameter.
2. Compute the standard error of the proportion.
3. Compute the margin of error of the proportion at 90% confidence level.
4. Find 90% and 95% confidence interval for all the female employees in the government agencies holding executive positions.
Problem: A marketing researcher randomly selects 20 female students in a certain university and found out that their
average monthly expenditures for their cell phone loads is Php 500.00 with a standard deviation of Php75.00
a. Find the 99% confidence interval for the average expenditures of female students for their cell phone loads.
b. Find the 90% confidence interval for the average expenditures of female students for their cell phone loads.
c. Find the 80% confidence interval for the average expenditures of female students for their cell phone loads.
3. Based from record, the population standard deviation of the monthly income of all newly hired IT graduates is Php500.00. A group of researchers surveyed 20 newly hired IT graduates and obtained a mean monthly income of Php33, 500.00. Assuming that their monthly income is approximately normally distributed, Find:
a. the point estimate of population
b. the margin of error if the confidence level is at 90%.
c. the 98% confidence interval of the monthly income of all the newly hired IT graduates.
4. XYZ University claims that some of their BS Accountancy first year students shifted to another course because of their retention policy, which is normally distributed. A random sample of 200 students revealed that 55 of them shifted to another course after their first year.
a. Compute the proportion estimate of the parameter.
b. Find the 95% confidence interval of the population proportion.
a) Determine the missing frequencies of the following distribution given that the median
is 33.5 and themode is 34.0.
Class limits 0-9 10-19 20-29 30-39 40-49 50-59 60-69 Total
Freq. 4 16 f3 f4 f5 6 4 230
b) Compute the arithmetic mean.
c) Compute the value below which 25% of the observations lie.
d) Compute the value above which 25% of the observations lie
#339914 on Dec 2023