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The Malayo Colleges Mindanao recently conducted a study analyzing the privacy management habits of teen internet users. In a group of 181 teens, 64 reported having more than 100 followers on Twitter. Find the point estimate of a 90% confidence interval for the true proportion of teens who would report having more than 100 followers on Twitter.





A coin is biased such that it is 1:2 for heads. If the coin is tossed 6 times, find the probabilities of obtaining various number of heads. 


Find the slope of the tangent line of the given function f below.





f(x)=x²+1

Find the slope of the tangent line of the given function f below.




f(x)=x²+1

Find the probability distribution of the random variable X, which can take only the values 1,2,3 given that P(1)=10/30,P(2)=1/3 and P(3)=12/33.


Two of the five (5) foreign automobiles from an overseas shipment have slight paint blemishes. If an agency receives three (3) of these automobiles at random, list the elements of the sample space 𝑆 using the letters B and N for “blemished” and “non-blemished”, respectively. For each sample point, assign a value 𝑥 of the random variable 𝑋 representing the number of automobiles purchased by the agency with paint blemishes


the weight of all male senior high school students from one province is measured and is found to be approximately normally distributed with a mean of 115 lbs and standard deviation of 3 lbs. find the percentile rank of the following weights?



A. 112 lbs



B. 115 lbs

On average 20% of the calculators produced in a factory are faulty. Samples of 10 calculators are to be selected at a random each day. Each calculator will be selected and replaced in the set of calculators which have been produced on that day. Calculate the probability that in any one sample, two calculators or less will be faulty. (4 marks)

Let P(x) denote the statement “x ≤ 4.” What are these truth values?

a) P(0)

b) P(4)

c) P(6)

d) P(5)

e) P (1)



A. Directions: Tossing four coins. Suppose four coins are tossed. Let Y be





the random variable representing the number of tails that occur. Complete





the table below by showing the values of random variable Y.





Let H = Heads





T = Tails

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