Math Answers

a school administrator claims that less than 50% of the students of sinapangan national high school are dissatisfied by the community canteen services.the claim by using sample data obtained from a survey of 500 students of the school where 54% indicated their dissatisfaction of the community canteen service.use a=0.05

activity 2 solve the following problems. show all your works. 1 in a study of the life expectancy of 500 people in a certain geographic region, the mean age at death was 720 years, and the standard deviation was 5.3 years. if a sample of 50 people from this region is selected, find the probability that the mean life expectancy will be less than 70 years.

Suppose that lifetimes of light bulbs produced by a certain company are normal random

variables with mean 1000 hours and standard deviation 100 hours. Suppose that

lifetimes of light bulbs produced by a second company are normal random variables

with mean 900 hours and standard deviation 150 hours. A person buys one light bulb

manufactured by the first company and one by the second company. What is the

probability that at least one of them lasts 980 or more hours?

Suppose that lifetimes of light bulbs produced by a certain company are normal random

variables with mean 1000 hours and standard deviation 100 hours. Suppose that

lifetimes of light bulbs produced by a second company are normal random variables

with mean 900 hours and standard deviation 150 hours. A person buys one light bulb

manufactured by the first company and one by the second company. What is the

probability that at least one of them lasts 980 or more hours?

1.     The owner of a theme park would like to know the average amount of time visitors spend there. To do this, he asked 25 of them and found out that they stayed for an average of 123.5 minutes with a standard deviation of 10.5 minutes. With a confidence level of 95 percent, determine the confidence interval estimate of the population mean.

Suppose we wish to test Ho: µ = 47 versus Ha: µ > 47. What will result if we conclude that the mean is greater than 47 when its true value is really 52?

Q: Suppose a dataset has 8500 email collection. Among 8500 emails, 4000 emails are not-spam and remaining are spam emails. The word “dating” is used as a feature, whose frequency/count in spam emails are 310 and 106 in not-spam emails. You have to compute two probabilities using bayes theorem, only knowing it contains the word “dating”.

First: Probability of an email being spam?        Second: Probability of an email being not spam?

Q: A certain virus infects one in every 20 people. A test used to detect the virus in a person delivers positive outcome at 85% accuracy for infected persons. Moreover, it provides negative outcome for healthy persons at 95% accuracy. Compute followings:

a)     Find the probability that a person has the virus given that his test outcome is positive.

b)     Find the probability that a person does not have the virus given that his test outcome is negative.

c)     Find the probability that a person has the virus given that his test outcome is negative.

3. A diet clinic states that there is an average loss of 24 pounds for those who stay on the program for 20 weeks. The standard deviation is 5 pounds. The clinic tries a new diet, reducing salt intake to see whether that strategy will produce a greater weight loss. A group of 40 volunteers loses as as average of 16.3 pounds each over 20 weeks. Should the clinic change the new diet? Use a 0.05

The owner of a factory that sells a particular bottled fruit juice claims that the average capacity of their products is 250 ml.to test the claim, a consumer group gets a sample of 100 such bottles, calculate the capacity of each bottle, and then the finds mean capacity to be 248 ml. The standard deviation is 5 ml. Is the claim true? Conduct a hypothesis testing using a=0.05.

1. Describe the population parameter of intersect.

2. Formulate the null and alternative hypothesis.

3.what is the appropriate form of test statistic to be used.

4. Identify the appropriate rejection region.

5.compute for the test statistic.(show solution)

6.Make a decision based on the computed value of z and the critical region.