![4Tris](/avatars/26428.jpg)
4Tris
30.04.2021 •
Mathematics
Y = |x – 3] + 2
Determine the transformation
Solved
Show answers
More tips
- C Computers and Internet Dropbox: What is it and How to Use it...
- H Health and Medicine How to Increase Hemoglobin in the Blood...
- A Animals and plants How to Store Carrots: Tips for Homeowners...
- L Legal consultation Juvenile Justice: Who Needs It?...
- F Family and Home How to Choose the Best Diapers for Your Baby?...
- F Family and Home Parquet or laminate, which is better?...
- L Leisure and Entertainment How to Properly Wind Fishing Line onto a Reel?...
- L Leisure and Entertainment How to Make a Paper Boat in Simple Steps...
- T Travel and tourism Maldives Adventures: What is the Best Season to Visit the Luxurious Beaches?...
- H Health and Medicine Kinesiology: What is it and How Does it Work?...
Answers on questions: Mathematics
- M Mathematics The graph shows the number of points, y, a player earns in a balloon game based on the number of balloons the player pops, x. Which of the following are the dependent quantities?...
- M Mathematics The price of stock increased by 2/3 cent Monday morning. On Monday Afternoon it decreased by 5/6 cent. On Tuesday mornin,the price increased by 3/4 cent. What is the overall...
- M Mathematics Melanie needs $500 for a down payment on a car. She is saving $50 per month. How many months will it take her to save $500? A. 5 months B. 10 monthsC. 15 monthsD. 20 months...
- M Mathematics I dont understand how to do this...
- M Mathematics What percent of 500 is 120? A. 12% B. 20% C. 24% D. 30%...
- M Mathematics Help pls for Show your work...
- M Mathematics A spinner with 8 sections is shown below. If you were to spin the spinner 200 times, how many times can you expect to land on yellow or purple?...
- M Mathematics There are 9 quarters 5 dimes 7 pennies 4 nickels A coin is drawn from a coin purse and spent. a second coin is drawn from the coin purse and spent. what is the probability...
- M Mathematics Help i need the work and i don’t know if this answer is right...
- M Mathematics Calculate the monthly payment need to pay off a $200,000 loan at 4% yearly interest over 20 year period. Recall that r is the monthly rate....
Ответ:
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Miguel is a golfer, and he plays on the same course each week. The following table shows the probability distribution for his score on one particular hole, known as the Water Hole.
Score 3 4 5 6 7
Probability 0.15 0.40 0.25 0.15 0.05
Let the random variable X represent Miguel’s score on the Water Hole. In golf, lower scores are better.
(a) Suppose one of Miguel’s scores from the Water Hole is selected at random. What is the probability that Miguel’s score on the Water Hole is at most 5 ? Show your work.
(b) Calculate and interpret the expected value of X . Show your work.
A potential issue with the long hit is that the ball might land in the water, which is not a good outcome. Miguel thinks that if the long hit is successful, his expected value improves to 4.2. However, if the long hit fails and the ball lands in the water, his expected value would be worse and increases to 5.4.
c) Suppose the probability of a successful long hit is 0.4. Which approach, the short hit or long hit, is better in terms of improving the expected value of the score?
(d) Let p represent the probability of a successful long hit. What values of p will make the long hit better than the short hit in terms of improving the expected value of the score? Explain your reasoning.
a) 80%
b) 4.55
c) 4.92
d) P > 0.7083
Step-by-step explanation:
Score | Probability
3 | 0.15
4 | 0.40
5 | 0.25
6 | 0.15
7 | 0.05
Let the random variable X represents Miguel’s score on the Water Hole.
a) What is the probability that Miguel’s score on the Water Hole is at most 5 ?
At most 5 means scores which are equal or less than 5
P(at most 5) = P(X ≤ 5) = P(X = 3) + P(X = 4) + P(X = 5)
P(X ≤ 5) = 0.15 + 0.40 + 0.25
P(X ≤ 5) = 0.80
P(X ≤ 5) = 80%
Therefore, there is 80% chance that Miguel’s score on the Water Hole is at most 5.
(b) Calculate and interpret the expected value of X.
The expected value of random variable X is given by
E(X) = X₃P₃ + X₄P₄ + X₅P₅ + X₆P₆ + X₇P₇
E(X) = 3*0.15 + 4*0.40 + 5*0.25 + 6*0.15 + 7*0.05
E(X) = 0.45 + 1.6 + 1.25 + 0.9 + 0.35
E(X) = 4.55
Therefore, the expected value of 4.55 represents the average score of Miguel.
c) Suppose the probability of a successful long hit is 0.4. Which approach, the short hit or long hit, is better in terms of improving the expected value of the score?
The probability of a successful long hit is given by
P(Successful) = 0.40
The probability of a unsuccessful long hit is given by
P(Unsuccessful) = 1 - P(Successful)
P(Unsuccessful) = 1 - 0.40
P(Unsuccessful) = 0.60
The expected value of successful long hit is given by
E(Successful) = 4.2
The expected value of Unsuccessful long hit is given by
E(Unsuccessful) = 5.4
So, the expected value of long hit is,
E(long hit) = P(Successful)*E(Successful) + P(Unsuccessful)*E(Unsuccessful)
E(long hit) = 0.40*4.2 + 0.60*5.4
E(long hit) = 1.68 + 3.24
E(long hit) = 4.92
Since the expected value of long hit is 4.92 which is greater than the value of short hit obtained in part b that is 4.55, therefore, it is better to go for short hit rather than for long hit. (Note: lower expected score is better)
d) Let p represent the probability of a successful long hit. What values of p will make the long hit better than the short hit in terms of improving the expected value of the score?
The expected value of long hit is given by
E(long hit) = P(Successful)*E(Successful) + P(Unsuccessful)*E(Unsuccessful)
E(long hit) = P*4.2 + (1 - P)*5.4
We want to find the probability P that will make the long hit better than short hit
P*4.2 + (1 - P)*5.4 < 4.55
4.2P + 5.4 - 5.4P < 4.55
-1.2P + 5.4 < 4.55
-1.2P < -0.85
multiply both sides by -1
1.2P > 0.85
P > 0.85/1.2
P > 0.7083
Therefore, the probability of long hit must be greater than 0.7083 that will make the long hit better than the short hit in terms of improving the expected value of the score.