Statistics and Probability Answers

In a given normal distribution, the population mean is 80 and the population standard deviation is 2.5. Find the corresponding z-score of the following values:

15. 84

If Z has a standard normal distribution, and P (0 < Z < z ) is 0.3770, then the

value of z is

Sample space of rolling a die

The average time it takes a group of senior high school students to

complete a certain examination is 46.2 minutes. The standard deviation is

8 minutes. Assume that the variable is normally distributed.

What is the probability that a random selected college student will

complete the examination in less than 43 minutes?

μ=220 grams σ=25 grams

If a mango is selected at random, what is the probability that its weight lies between 180 and 250 grams?

In a certain Algebra 2 class of 28 students, 14 of them play basketball and 7 of them play baseball. There are 2 students who play both sports. What is the probability that a student chosen randomly from the class plays basketball or baseball?

A fitness center claims that its members lose an average of 12 pounds or more the first month after joining the center. An independent agency that wanted to check this claim took a sample of 45 members and found that they lost an average of 10 pounds within the first month with standard deviation of 3 pounds. Find the p-value for this test. What will your decision be if 𝛼 = 0.05?

 A report in LTO stated that the average age of taxis in the Philippines is 12 years. An operations manager of a large taxi company selects a sample of 40 taxis and finds the average age of the taxis is 11.2 years. The standard deviation of the population is 2.3 years. At 0.05 level of significance, can it be concluded that the average age of the taxis in his company is less than the national average?

Average Senior High School annual cost of tuition fee for all private schools last year was P46,300. A random sample of costs this year for 45 private schools indicated that the sample mean was P47,800 and a sample standard deviation was P5,600. At the 0.10 level of significance, is there sufficient evidence to conclude that the cost has increased?

A TV manufacturer claims that the life span of its regular TV sets is 12 years with a standard

deviation of 1.2 years. Using a random sample of their 20 TV sets, the average life span is found

to be 11.2 years. Test the hypothesis that the T sets’ life span of 12 years as claimed by the

manufacturer is true at 0.05 level.