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Martha, Andre, Erika, Donald, and Jane are running for 12th grade class offices. They will be named to the positions of president, vice-president, secretary, treasurer, and parliamentarian according to the number of votes each receives. The person with the most votes will be president, the person with the second-highest number of votes will be vice-president, and so on. In how many different ways can the five students form a set of class officers?
2) A,B and C are three events. Express the following events in set notations. (10)
(i) Simultaneous occurrence of A,B and C.
(ii) Occurrence of at least one of them.
(iii) Both A and B occur and C does not occur.
(iv) The event B but not A occurs.
(v) Not more than one of the events A,B and C occur.
A company estimates that about 0.7% of their products will fail after the regular one-year warranty but within two years from the date of purchase. If this happens, the company will pay a replacement cost of 3500. If the company offers its customers an extended warranty covering a period of two years for the price of 480.
According to a study done last year, the average monthly expenses for cell phone loads of high school students in Manila was P350.00. A Statistics student believes that this amount has increased since January of this year. Is there a reason to believe that this amount has really increased if a random sample of 60 students has an average monthly expenses for cell phone loads of P380.00? Use 0.05 level of significance. Assume that the population standard deviation is p77.00.
A visiting school inspector asked a class teacher to rank the thirty students in her class on “level of discipline”, with 1 standing for the least disciplined student and 30 standing for the most disciplined student
Consider the experiment of tossing a coin three times (Prob. 1.1). Let X be the random variable giving the number of heads obtained. Assume that the tosses are independent and the probability of a head is p. (a) What is the range of X? (b) Find the probabilities P(X = 0), P(X = I), P(X = 2), and P(X = 3).
In a Science test, the mean score is 42 and the standard deviation is 5. Assuming the scores are normally distributed, what is the probability that the score is:
C. between 30 and 48?
1. Convert the raw score of 48 to a z-score.
2. Draw the normal curve and locate the given z-value or values at the base line of the curve. Then, draw a vertical line through the given z-value or values and shade the required region.
3. Use the table and find the area that corresponds to the computed z-score.
4. Examine the shaded region and make an appropriate operation to apply, if needed.
5. Make a concluding statement.
In a Science test, the mean score is 42 and the standard deviation is 5. Assuming the scores are normally distributed, what is the probability that the score is:
B. less than 50?
1. Convert the raw score of 50 to a z-score.
2. Draw the normal curve and locate the given z-value or values at the base line of the curve. Then, draw a verticalline through the given z-value or values and shade the required region.
3. Use the table and find the area that corresponds to the computed z-score.
4. Examine the shaded region and make an appropriate operation to apply, if needed
5. Make a concluding statement.
You already know how to convert a random normal variable to a standard normal score or z-score. This time, let’s do the reverse. Given the z-score, compute for the raw scores. Problem number is done as an example to guide you. Problems 2 and 3 are given to you.
2. Given: 𝑥 = 75, 𝑠 = 10. What is the raw score when 𝑧 = −1.56?
1. Use the computing formula for finding the z-score for sample data. You can derive the formula for easy computation.
2. Write the given values
4. Substitute the given values in the computing formula. Then, compute the raw score (𝑥).
3. Given: 𝜇 = 48,𝜎 = 5.5. What is the raw score when 𝑧 = 2.43?
1. Use the computing formula for finding the z-score for sample data. You can derive the formula for easy computation.
2. Write the given values.
3. Substitute the given values in the computing formula. Then, compute the raw score (𝑥).
How many premutations of the letters of the word " BAHRAIN" end with "R"?
