It has been found that times taken by people to complete a particular tax form follow a normal distribution with a mean of 100 minutes and a standard deviation of 30 minutes.a. What is the probability that a randomly chosen person takes less than 85 minutes to complete this form?b. What is the probability that a randomly chosen person takes between 70 and 130 minutes to complete this form?c. Five percent of all people take more than how many minutes to complete this form?d. Two people are chosen at random. What is the probability that at least one of them takes more than an hour to complete this form?e. Four people are chosen at random. What is the probability that exactly two of them take longer than an hour to complete this form?f. For a randomly chosen person, state in which of the following ranges (expressed in minutes) the time to complete the form is most likely to lie.70-89, 90-109, 100-129, 130-149g. For a randomly chosen person, state in which of the following ranges (expressed in minutes) the time to complete the form is least likely to lie.70-89, 90-109, 110-129, 130-149
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!
It has been found that times taken by people to complete a particular tax form follow a
a. What is the probability that a randomly chosen person takes less than 85 minutes to complete this form?
b. What is the probability that a randomly chosen person takes between 70 and 130 minutes to complete this form?
c. Five percent of all people take more than how many minutes to complete this form?
d. Two people are chosen at random. What is the probability that at least one of them takes more than an hour to complete this form?
e. Four people are chosen at random. What is the probability that exactly two of them take longer than an hour to complete this form?
f. For a randomly chosen person, state in which of the following ranges (expressed in minutes) the time to complete the form is most likely to lie.
70-89, 90-109, 100-129, 130-149
g. For a randomly chosen person, state in which of the following ranges (expressed in minutes) the time to complete the form is least likely to lie.
70-89, 90-109, 110-129, 130-149
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