Question

a) Consider a gamble with a 40% chance of winning $10 and a 60% chance of losing $10. What is the standard deviation of this gamble? b) An analysis of past reservations at a hotel finds that on any given day, of all the travelers who book a room, 6% of them do not show up at the hotel that day. If 200 travelers have reservations today, what is the mean and standard deviation of the number of travelers who are expected to show up at the hotel today? Assume each traveler's chance of missing their hotel reservation is independent of all other travelers, and the chance of missing their hotel reservation is the same for all travelers. Mean = 188 travelers; standard deviation = 3.4 travelers c) On any given day when I am on vacation, the chance I run is 25%. On any given day when I am not on vacation, the chance I run is 50%. The chance I run on any given day is 40%. On a randomly chosen day, what is the probability I run or I am on vacation? a. 80% b. 70% c. 65% d. 60% e. 50% 

          a) Consider a gamble with a 40% chance of winning $10 and a 60% chance of losing $10. What is the standard deviation of this gamble?
b) An analysis of past reservations at a hotel finds that on any given day, of all the travelers who book a room, 6% of them do not show up at the hotel that day. If 200 travelers have reservations today, what is the mean and standard deviation of the number of travelers who are expected to show up at the hotel today? Assume each traveler's chance of missing their hotel reservation is independent of all other travelers, and the chance of missing their hotel reservation is the same for all travelers.
Mean = 188 travelers; standard deviation = 3.4 travelers
c) On any given day when I am on vacation, the chance I run is 25%. On any given day when I am not on vacation, the chance I run is 50%. The chance I run on any given day is 40%. On a randomly chosen day, what is the probability I run or I am on vacation?
a. 80% b. 70% c. 65% d. 60% e. 50%
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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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a) Consider a gamble with a 40% chance of winning $10 and a 60% chance of losing $10. What is the standard deviation of this gamble? b) An analysis of past reservations at a hotel finds that on any given day, of all the travelers who book a room, 6% of them do not show up at the hotel that day. If 200 travelers have reservations today, what is the mean and standard deviation of the number of travelers who are expected to show up at the hotel today? Assume each traveler's chance of missing their hotel reservation is independent of all other travelers, and the chance of missing their hotel reservation is the same for all travelers. Mean = 188 travelers; standard deviation = 3.4 travelers c) On any given day when I am on vacation, the chance I run is 25%. On any given day when I am not on vacation, the chance I run is 50%. The chance I run on any given day is 40%. On a randomly chosen day, what is the probability I run or I am on vacation? a. 80% b. 70% c. 65% d. 60% e. 50%
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Transcript

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00:01 Hello, let's have a look on the question.
00:03 So for the a part, we have let x be the given random variable.
00:09 So it is given to us that probability of x is equal to 10 is equal to 0 .4 and probability that x is equal to minus 10 is equal to 0 .6.
00:18 So these are the probabilities that are given to us.
00:21 So when we calculate the expectation, so expectation of x will be equal to probability of x equal to 10 multiplied by 10 plus probability of x.
00:31 X is equal to minus 10 multiplied by minus 10.
00:37 So this is equal to 0 .4 multiplied by 10 plus this is 0 .6 multiplied by minus 10.
00:44 This will be equal to 4 minus 6 that is equal to minus 2.
00:48 So from here we can see that expectation of x is equal to minus 2.
00:52 Now we need to calculate expectation of x square.
00:56 So this will be equal to probability that x is equal to 10 multiplied by 10 square plus probability that x is equal to minus 10 multiplied by minus 10 whole square.
01:08 So this is 0 .4 multiplied by 100 plus 0 .6 multiplied by 100...
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