2.1 Random Variables
If the time in minutes it takes to complete a task can be any non-negative value, is it a discrete or continuous random variable?
This is a continuous random variable, as it can take on an infinite number of values in a given range.
A survey said that 78% of the population likes rice. A sample of 10 people is selected. Let X represent the number of people who like rice. What's the probability that half of the selected sample likes rice?
0.03749617
The time between bus arrivals follows an exponential distribution with a mean of 7 minutes. What is the probability that the time taken is exactly 5 minutes?
0
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In a survey of 60 people, the number of books read last year is distributed as follows:
0 books: 10 people
1 book: 20 people
2 books: 15 people
3 books: 10 people
4 books: 5
What is its expected value?
100/60 which is approximately 1.6667
In a school lottery, there are 20 students, 12 of whom are athletes. The principal randomly selects four students to help with an event. Let X represent the number of athletes chosen. What's the probability that at least 2 athletes will be selected?
0.8468524
Suppose a beetroot farmer's field produces 0.5 a beet per 15 days, what is the probability that less than 10 days will pass between successive beets?
0.2834687
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For the same survey as above, calculate its Standard Deviance.
1.3889
Suppose in a farmer's potato field, the average number of potatoes per acre is 4. Suppose that an acre is randomly selected; what is the probability of there being at least 2 potatoes?
0.7618967
What is a standardized score or z-score?
It expresses value x (that variable X can attain), in terms of how many standard deviations away from the mean it is. Useful for analyzing data.
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Let X be a random variable with VAR(X) = 9. What is VAR(3X +4)?
81
If the average number of potatoes per acre is 5, what is the average number of potatoes per half acre?
2.5
Suppose the time taken for potatoes to grow is modeled by a normal distribution with a mean of 15 days, and a standard deviation of 4 days. Let X represent the number of days when a potato is fully developed. What is the 60th percentile days taken (value at our variable for which 60% of observations fall below)?
16.01339
What does PTSD stand for?
Post-Traumatic Down Syndrome