Acarsalespersonestimatesthefollowingprobabilities forthenumberofcarsthatshewillsellinthenextweek: Numberofcars 0 1 2 3 4 5 Probability 0.10 0.20 0.35 0.16 0.12 0.07 a. Find the expected number of cars that will be sold in the week. b. Find the standard deviation of the number of cars that will be sold in the week. c. The salesperson receives a salary of $250 for the week, plus an additional $300 for each car sold. Find the mean and standard deviation of her total salary for the week. d. What is the probability that the salesperson’s sal- ary for the week will be more than $1,000?
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!
Acarsalespersonestimatesthefollowingprobabilities forthenumberofcarsthatshewillsellinthenextweek:
Numberofcars 0 1 2 3 4 5
Probability 0.10 0.20 0.35 0.16 0.12 0.07
a. Find the expected number of cars that will be sold in the week.
b. Find the standard deviation of the number of cars that will be sold in the week.
c. The salesperson receives a salary of $250 for the week, plus an additional $300 for each car sold. Find the mean and standard deviation of her total salary for the week.
d. What is the probability that the salesperson’s sal- ary for the week will be more than $1,000?
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