Expected Value
A company makes electronic gadgets. One out of every 50 gadgets is faulty, but the company doesn't know which ones are faulty until a buyer complains. Suppose the company makes a $3 profit on the sale of any working gadget, but suffers a loss of $80 for every faulty gadget because they have to repair the unit. Check whether the company can expect a profit in the long term.
Yes, expected value of 1.34
The sum of standard deviations would be the same as the difference between standard deviations when combining random variables. True or False?
True
SD = sqrt(SDX^2 + SDY^2).
What are the 4 truths that must be observed for us to be able to use a binomial formula?
Each trial is independent from the others.
There are a discrete (countable) number of trials.
Each trial must have the same probability of success, denoted as p.
Each trial must be able to be defined as either a success or a failure
A coin is weighted so that the probability of heads is 0.64. What is the probability that the first heads will appear on the 3rd flip?
.0829
What was the name of the robot maid from "The Jetsons"?
Rosie
Marciel is considering buying a flood insurance policy for the upcoming year that costs 600 dollars and receives 50,000 dollars if her home floods. Based on previous years, she estimates that there is a 2% chance of her home flooding this year.
Find the expected value of buying this flood insurance policy.
-600(.98) + (49,400)(.02) = $400
A large bakery uses a machine to dispense frosting onto its cookies. A certain type of cookie gets 4 dots of frosting on top of each cookie. The dots of frosting have a mean mass of mu=3grams and a standard deviation of sigma=0.25 grams. We can assume that the masses of the dots of frosting are independent from each other. Let T be the total mass of the dots of frosting on a randomly chosen cookie.
Find the mean of T.
12 grams
Biologists breed a pair of plants where each plant has the color genes Gg. This means that any offspring these plants produce has a 25% chance of inheriting the color genes gg, which makes the offspring an albino plant. Assume that offspring inherit genes independently from each other.
What would be the probability of this pair producing exactly 1 albino plant among 6 offspring?
.356
What are the 4 rules for a geometric setting?
1. Either a success or failure
2. Trials are independent
3. Probabilities are the same for each trial
4. The variable of interest is the number of trials until the first success
Can you name 5 countries of Eastern Europe?
Estonia, Latvia, Lithuania, Czech Republic, Slovakia, Slovenia, Hungary, Ukraine, Moldova
Kelsie works at a bicycle shop as a salesperson. She records the number of bicycles she sells on a daily basis. Here is the probability distribution of the [T=] the time she spends filling out daily sales reports.
T=time (minutes)[0] [10] [20] [30]
Probability [0.30] [0.50 ] [0.15] [0.05]
Find the expected value of the amount of time Kelsie spends filling out daily sales reports.
9.5 Minutes
Andy and Jim are going to compete in the 100-meter dash against each other. Let A be the time it takes Andy to complete the race, and J be the time it takes Jim to complete the race. Based on previous results, they know that [mu_A=11.5] seconds and [sigma_A=1] second. They also know that [mu_J=10.5] seconds and [sigma_J=0.5] seconds.
Assume that their times are independent. Let [D] be the difference between their times in a random 100-meter dash [(D=A-J)].
Find the standard deviation of [D].
1.118
An online retailer offers next-day shipping for an extra fee. The retailer says that 65% of customers who pay for next-day shipping actually receive the item the next day, and those who don't are issued a refund. Suppose we take an SRS of 20 next-day orders, and let X represent the number of these orders that arrive the next day. Assume that the arrival statuses of orders are independent.
What is the probability that 18 of those customers got their orders the next day?
.01 or .009985
Find the mean and standard deviation of a geometric distribution, where the probability of success is .06.
Mean: 16.67
Standard Deviation: 16.16
What name is singer-actor Stefani Germanotta better known by?
Lady Gaga
You draw one card from a standard stack of playing cards. If you pick a heart you win $15. If you pick a face card, which is not a heart, you win $10. If you pick any other card, you lose $7. Do you want to play?
Yes, expected value would be $1.44
Ahmad and Bryson are in a long-term fitness challenge that involves counting how many calories they consume on daily basis. Let [A=] the number of calories Ahmad consumes daily, and [B=] the number of calories Bryson consumes daily. Based on previous data, they know that [mu_A=2200] calories and [sigma_A=300] calories. They also know that [mu_B=2400] calories and [sigma_B=400] calories.
Assume that their daily calorie counts are independent, and let [D] be the difference between the number of calories they each consume on a randomly selected day [(D=B-A)].
Find the mean of [D].
200 calories
Salim has a flock of 300 chickens, 15% of which are infected with a virus. He plans on taking an SRS of 7 chickens to test for the virus.
What would be the probability that 4 or more of the 7 chickens sampled have the virus?
.012
A basketball player has a 60% chance of making his foul shots during the season. Assuming the shots are independent, find the probability that he misses for the first time on his 3rd shot.
.144
Name 3 80's or 90's Boy Bands
NSYNC, Backstreet Boys, New Kids on the Block, Marky Mark and the Funky Bunch, 98 Degrees, Boyz II Men
You roll a 6-sided dice. If you roll 5-6, you get $5,000,000. If you roll 1-4, you have to pay $1,000,000. If you could play this game only once, would you? Why or why not?
If I could play only once, I would not. Expected Value is what we get in the long run. There is high variability in this instance and it is not worth the one shot deal, even though the expected value is profitable.
Ahmad and Bryson are in a long-term fitness challenge that involves counting how many calories they consume on daily basis. Let [A=] the number of calories Ahmad consumes daily, and [B=] the number of calories Bryson consumes daily. Based on previous data, they know that [mu_A=2200] calories and [sigma_A=300] calories. They also know that [mu_B=2400] calories and [sigma_B=400] calories.
Assume that their daily calorie counts are independent, and let [D] be the difference between the number of calories they each consume on a randomly selected day [(D=B-A)].
Find the standard deviation of [D].
500 calories
Aja's favorite cereal is running a promotion that says 1-in- 4 boxes of the cereal contain a prize. Suppose that Aja is going to buy 5 boxes of this cereal, and let X represent the number of prizes she wins in these boxes. Assume that these boxes represent a random sample, and assume that prizes are independent between boxes.
What is the probability that she wins at most 1 prize in the 5 boxes?
.6328
A target shooter makes 65% of the shots she takes. What is the probability that her first success is after the 5th shot she takes?
.0052
What actor-comedian found fame on the TV show “Mork and Mindy?
Robin Williams