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The average lifetime of 120 Brand X Alkaline AA batteries and 120 Brand Y alkaline AA batteries were found to be 9.1 hours and 9.6 hours respectively. Suppose the standard deviations of lifetimes are 1.9 for Brand X batteries and 2.1 hours for Brand Y batteries, test the hypothesis using α = 0.05
Tn=5n-4
An aptitude test for selecting officers in a bank was conducted on 1,000 candidates, the average score is 42 and the standard deviation of scores is 24. Assume that the scores are normally distributed, answer the following questions.
i. What is the probability that the candidates score,
A.Exceed 65?
B.Between 40 and 60?
ii. Find the number of candidates whose score,
A. Exceed 40?
B. Lie between 40 and 65?
An aptitude test for selecting officers in a bank was conducted on 1,000 candidates, the average score is 42 and the standard deviation of scores is 24. Assume that the scores are normally distributed, answer the following questions.
i. What is the probability that the candidates score,
A. Exceed 65?
B. Between 40 and 60?
ii. Find the number of candidates whose score,
A. Exceed 40?
B. Lie between 40 and 65?
The following population is provided:17, 15, 8, 9, 7, 9, 11, 12, 14, 16, 9, 5, 10, 14, 13, 12, 12, 11, 9, 14, 8, 14, 12. Further, a simple random sample from this population gives the following values: 12, 9, 5, 10, 14, 11. Compute the sampling error for the sample mean.
a. 1.811 b. 1.167 c. 1.181 d. 1.348 e. None of the above
Thirty people, who are of the same age and the same health status, are
insured with the same insurance company. Using life tables, the company
estimates that the probability for a randomly chosen person among these 30
to be alive in 15 years from now is 0:8.
(i) What is the probability that not all 30 people will be alive in 15 years time?
(ii) What is the probability that at least one person will be alive?
Verify that each of the following statements is a false statement by finding a counterexample for each.
- xx=1
- x+33=x+1
- x2+16=x+4
The probability that a car is stolen when it is parked overnight in an unsafe
area of a city is 10%. If there are 12 cars parked on a particular street of that
area, what is the probability that during a night
(i) no car is stolen?
(ii) at most two cars are stolen?
(iii) at least nine cars are stolen?
Wanda, Loki, Natasha, and Stephen were recently elected as the new class officers (president, vice
president, secretary, treasurer) of the sophomore class at Marvel College. From the following clues,
determine which position each holds.
1. Stephen is younger than the president but older than the treasurer.
2. Wanda and the secretary are both the same age, and they are the youngest members of the
group.
3. Natasha and the secretary are next door neighbors.
Determine whether each of the following arguments is an example of inductive reasoning or deductive
reasoning.
a. All Janet Evanovich novels are worth reading. The novel To the Nines is a Janet Evanovich
novel. Thus To the Nines is worth reading.
b. I know I will win a jackpot on this slot machine in the next 10 tries, because it has not paid out
any money during the last 45 tries.
