Statistics and Probability Answers

2.1 Suppose P(A) = 0.75 and P(B) = 0.82. Find the following:

2.1.1 P (A and B) if A and B are independent. (2)

2.1.2 P (not A and not B), if A and B are independent. (2)

2.1.3 P (A and B), if A and B are mutually exclusive. (1)

2.2 Solve the following inequality. (3)

x2 - 5x + 6 ≥ 0

Conduct a traditional hypothesis test for the null hypothesis H0: µ = 100 against the alternative

hypothesis H1: µ > 100 based on the 35 random observations. The sample mean is 105 and the

sample standard deviation is 15. Use α = 0.01.

The average height of all entering freshmen students is 165 cm with the standard deviation

. To test the claim, a researcher selected a random sample of 50 freshmen of a certain

college. In this sample, and . Is the claim true?

What is statistics

What is the 5th percentile of a

t

-distribution whose sample size is 23?

A company produces mosquito repellants that have a period of effectiveness that is approximately normally distributed with a mean of 300 hours and a standard deviation of 30 hours. A sample of 40 repellants was taken and the average period of effectiveness is computed as 290 hours. Is this sufficient evidence to conclude that the company’s claim is true at α=0.01?

The owner of a fast-food shop claims more than 45% of the household within 5-kilometer radius of the fast-food shop have at least one member who eats at the fast-food shop at least once a week. In a sample of 250 households in the area, an investigator found that members of 180 households did so. Do these data provide sufficient evidence to support the fast-food shop owner’s claim? Use 90% level of confidence.

soft drink dispenser is designed to dispense 250 mL of drink per cup. However, there have

been recent reports to the managements of a fast-food restaurant of both underfilled and

overfilled cups. Seeking to investigate this matter, they fill up 40 cups using this machine. If the mean amount of drink in the 40 cups is 245 mL with standard deviation of 10 mL, is there a

cause for concern for the management? Use a level of significance of 0.01

 Identify the critical value of each given problem. Find the rejection region and sketch the curve on a separate sheet of paper.

“According to the radio announcer, the average price of kilogram of pork liempo is more than ₱210.00. However, a sample of 15 prices randomly collected from different markets showed an average of ₱215.00 and standard deviation of ₱9.00. Using 0.05 level of significance, is there sufficient evidence to conclude that the average price of pork liempo is more than ₱210.00?”

A coffee vending machine is designed to dispense 180 ml of coffee but its owner 

suspects that it is dispensing more than what is designed for. He took a random 

sample of 40 and found out that the mean is 192 ml with a standard deviation of 

4 ml. do you think the owner is right about his suspicion? Test at 0.05 level of 

significance.