Statistics and Probability Answers

A study believes that 70% of adults in the Philippines own a cellphone.

A cellphone manufacturer believes that the actual number is much

less than 70%. 100 Filipino adults were surveyed, of which 74 have

cellphones. Using a 5% level of significance, is the cellphone

manufacturer’s claim valid or not?

The letters in the word TRIANGLE are to be arranged. How many ways can these letters be arranged in a line such that letters E and G appear in adjacent positions?

It is the decision when the value of the test statistics lies within the critical region

Let X be a continuous random variable such that 𝑓(𝑥) =1, 𝑓or 𝑓 0<𝑋<1.

Find the following probabilities:

1. 𝑃(𝑋>0.5)
2. 𝑃(0.5<𝑋<0.8)

A manufacturer claims that the average lifetime of his lightbulb is

3 years or 36 months. The standard deviation is 8 months. Fifty bulbs are selected, and the average life expectancy is found to be 32 months. Should the manufacturer statement be rejected at level of significance 0.01?

A group of 8 students in your class having the weight of 50, 52, 53, 54, 56, 57 58, and 60.

You are the manager of a fast-food restaurant. The business problem is to determine

whether the population mean waiting time to place an order has changed in the past month

from its previous population mean value of 4.5 minutes. From past experience, you can

assume that the population is normally distributed, with a population standard deviation of

1.2 minutes. You select a sample of 36 orders during a one-hour period. The sample mean is

5.1 minutes. To test this statistical hypothesis, with a = 0.05

you have then testing hypothesis (null and alternate hvpothesises) is

A sample of 60 Grade 9 students’ ages was obtained to estimate the mean age of all Grade 9 students. Sample mean of 15.3 years and the population standard deviation is 4. What is the point estimate of the population mean

Consider the sample 14, 19, 18, 20, 16, 9, 10, 6, and 8. Find the mean.

two good dice are rolled simultaneously. let a denote the event “ the sum shown is 8" and b the event “the two show the same number". find p(a), p(b), p(a ∩ b), and p(a ∪ b).