Statistics and Probability Answers

Consider the case where the predetermined average number of bus arrivals at the Cubao Station is 6 per 15-minute period. Find the pro of at least 4 buses arriving in a 15-minute period.

Observe yourself in a day. Find out how many hours you spend in the following activities: house chores, answering Self Learning Modules, 

3. The time taken to assemble a car in a certain plant has a normal distribution with mean of 25.4 hours and a standard deviation of 4.1 hours. Calculate the probability that a car can be assembled at this plant in the following period of time:

a) More than 28.8 hours

b) Between 18.6 and 27.5 hours

c) Between 25.0 and 34.0 hours

2. A researcher wishes to test the claim of a particular cereal manufacturer that the mean weight of cereal in the boxes is less than 300g. A sample of 50 boxes yields a sample mean weight of 296g. Assume that the population standard deviation is 5g.

a) Can we conclude that the claim is true? Test at α = 0.05.

b) Obtain a 95% confidence interval for μ.

1. A company sells packets of durian crackers that they claim on average, contains at least 20g of durian crackers. They admit that their claim is wrong (and will refund any money), if a sample of 40 durian crackers have a mean less than 19.8g. If the standard deviation is 0.5g, determine the critical value that specifies the rejection region.

Scenario: In a study looking at undergraduate students’ perceptions of sense of community at their university, a researcher hypothesizes that the farther away students live from campus (in miles), the less they feel they are part of the university community. The researcher collected data for the following two variables – miles from campus and part of community (rating from 1-10 of how much they felt part of the university community).

Datafile: community.xlsx

If the time between calls in a call center follows an Exponential Distribution with mean 5 minutes, what is the probability that there will not be another call in the next 10 minutes?

If there are 10 candidate materials that can be used for manufacturing a certain machine and the probability that each one leads to a machine that lasts at least 10 years is 0.8, what is the probability that exactly 7 of the machines will last at least 10 years?

For a standard Normal random variable find the following probabilities. a. X is less than 1.72

b. X is less than -0.88

c. X is between 1.30 and 1.75

d. X is between -0.25 and 0.45

If a random variable is normally distributed with mean 4.35 and standard deviation 0.59, what is the probability that this random variable will take on values more than 5.2?