a) What is the probability that a person selected at random spends more than 60 minutes on social media? b) Of the people, 95% spend less than Th minutes on social media. Find the value of Th. c) As you have learned in the lecture, a normally distributed random variable also takes negative values as it is defined over (-∞,+∞). Why do many random variables that take only positive values, like the one in this question, can still be assumed to have a normal distribution?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Suppose that time spent by a group of people on social media follows a
normal distribution with a mean of 75 minutes and a standard deviation of 10 minutes.
a) What is the probability that a person selected at random spends more
than 60 minutes on social media?
b) Of the people, 95% spend less than Th minutes on social media. Find the
value of Th.
c) As you have learned in the lecture, a
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