A municipal bus company has started operations in a new subdivision. Records were kept on the numbers of riders on one bus route during the early-morning weekday service. The accompanying table shows proportions over all weekdays.Number of riders 20 21 22 23 24 25 26 27Proportion 0.02 0.12 0.23 0.31 0.19 0.08 0.03 0.02a. Graph the probability distribution.b. Calculate and graph the cumulative probability distribution.c. What is the probability that on a randomly chosen weekday there will be at least 24 riders from the subdivision on this service?d. Two weekdays are chosen at random. What is the probability that on both of these days there will be fewer than 23 riders from the subdivision on this service?e. Find the mean and standard deviation of the number of riders from this subdivision on this service on a weekday.f. If the cost of a ride is $1.50, find the mean and standard deviation of the total payments of riders from this subdivision on this service on a weekday.
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!
A municipal bus company has started operations in a new subdivision. Records were kept on the numbers of riders on one bus route during the early-morning weekday service. The accompanying table shows proportions over all weekdays.
Number of riders 20 21 22 23 24 25 26 27
Proportion 0.02 0.12 0.23 0.31 0.19 0.08 0.03 0.02
a. Graph the
b. Calculate and graph the cumulative probability distribution.
c. What is the probability that on a randomly chosen weekday there will be at least 24 riders from the subdivision on this service?
d. Two weekdays are chosen at random. What is the probability that on both of these days there will be fewer than 23 riders from the subdivision on this service?
e. Find the mean and standard deviation of the number of riders from this subdivision on this service on a weekday.
f. If the cost of a ride is $1.50, find the mean and standard deviation of the total payments of riders from this subdivision on this service on a weekday.
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