Statistics and Probability Answers

Explain how the value of the median is determined for a data set that contains an odd number of ob-

servations and for a data set that contains an even number of observations.

The average time it takes a group of college students to complete a certain examination is 32 minutes. The standard deviation is 6 minutes. Assume that the variable is normally distributed.

If 64 randomly selected college students take the examination, what is the probability that the mean time it takes the group to complete the test will be less than 36 minutes?

Explain the usefulness of central limit theorem in solving problems involving sampling

Three lottery tickets for first, second, and third prizes

Two of the five (5) foreign automobiles from an overseas shipment have slight paint blemishes. If an agency receives three (3) of these automobiles at random, list the elements of the sample space 𝑆 using the letters B and N for “blemished” and “non-blemished”, respectively. For each sample point, assign a value 𝑥 of the random variable 𝑋 representing the number of automobiles purchased by the agency with paint blemishes.

Three lottery tickets for first, second, and third prizes are drawn from a group of 45 tickets

the mean weight of baggage of 25 passengers from USA bound for the Philippines is 31.8 kilos with a variance of 16. test the claim that the population mean baggage weight is equal to 30 kilos at 0.01 level of significance. Assume that the population is normally distributed. The t value is 2.492

2. Average Senior High School annual cost of tuition fee for all private schools last year was Php43,700. A random sample of costs this year for 45 private schools indicated that the sample mean was Php45,800 and a sample standard deviation was Php5,600. At 0.01 level of significance, is there sufficient evidence to conclude that the cost increased? Solution: Step 1: State the hypothesis. 𝐻0: _____________________________________________________________ 𝐻1: _____________________________________________________________ Step 2: The level of significance and critical region. 𝛼 = ________ and the 𝑧𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 = __________ Step 3: Compute for the value of one sample t test. 𝑧𝑐𝑜𝑚𝑝𝑢𝑡𝑒𝑑 = _______ Step 4: Decision Rule. ________________________________________________________________ ___________________________________. Step 5: Conclusion: _______________

Consider a population consisting of 1,2,3,4 and 5. Supposed samples of size 3 are drawn from this population.Find the sampling distribution of the sample means.

what is the lowest valeu of the sample mean in this sampling distribution