Question

In: Math

The developers of a new online game have determined from preliminary testing that the scores of...

The developers of a new online game have determined from preliminary testing that the scores of players on the first level of the game can be modelled satisfactorily by a Normal distribution with a mean of 185 points and a standard deviation of 28 points. They would like to vary the difficulty of the second level in this game, depending on the player’s score in the first level.

(a) The developers have decided to provide different versions of the second level for each of the following groups:

(i) those whose score on the first level is in the lowest 25% of scores

ii) those whose score on the first level is in the middle 50% of scores

(iii) those whose score on the first level is in the highest 25% of scores. Use the information given above to determine the cut-off scores for these groups. (You may round each of your answers to the nearest whole number.)

(b) In the second level of the game, the developers have also decided to give players an opportunity to qualify for a bonus round. Their stated aim is that players from group (i) should have 75% chance of qualifying for the bonus round, players from group (ii) should have 55% chance of qualifying for the bonus round and that players from group (iii) should have 30% chance of qualifying for this round. Let ?, ? and ? respectively denote the events that a player’s score on the first level was in the lowest 25% of scores, the middle 50% of scores and the highest 25% of scores, and let ? denote the event that the player qualifies for the bonus round. Use event notation to express the developers’ aim as a set of conditional probabilities.

(c) Based on the developers’ stated aim, find the total probability that a randomly chosen player will qualify for the bonus round.

(d) Given that a player has qualified for the bonus round, what is the probability that the player’s score on the first level was in the middle 50% of scores for that level?

(e) Given that a player has not qualified for the bonus round, what is the probability that the player’s score on the first level was in the lowest 25% of scores for that level?

Solutions

Expert Solution

Please rate. Cheers !!


Related Solutions

After preliminary testing, it is determined that .01 of the residents of Selma have a certain...
After preliminary testing, it is determined that .01 of the residents of Selma have a certain virus. In Sangrian, a suburb of Selma (incidence of the virus is the same), the authorities test the 10,000 residents of the suburb. The test has the following characteristics. If you have the virus, the probability that the test is positive is .95, and if you don’t have the virus, the probability that the test is positive is .10. Suppose that 1,100 of the...
JAVA - Programming Exercise 10-5. The developers of a free online game named Sugar Smash have...
JAVA - Programming Exercise 10-5. The developers of a free online game named Sugar Smash have asked you to develop a class named SugarSmashPlayer that holds data about a single player. The class contains the following fields: idNumber - the player’s ID number (of type int) name - the player's screen name (of type String) scores - an array of integers that stores the highest score achieved in each of 10 game levels Include get and set methods for each...
A video game developer is testing a new game on three different groups. Each group represents...
A video game developer is testing a new game on three different groups. Each group represents a different target market for the game. The developer collects scores from a random sample from each group. The results are shown below Group A Group B Group C 97 152 99 103 148 110 95 161 198 110 112 183 106 129 155 That is the mean sum of squares Between  MS(Between)?
20. A video game developer is testing a new game on three different groups. Each group...
20. A video game developer is testing a new game on three different groups. Each group represents a different target market for the game. The developer collects scores from a random sample from each group. Show all work to receive credit. Include a table of your results. Group A Group B Group C 101 151 101 108 149 109 98 160 198 107 112 186 111 126 160 What is the df(Between)? What is the df(Within)? What are the SSbetween...
A video game developer is testing a new game on three different groups. Each group represents...
A video game developer is testing a new game on three different groups. Each group represents a different target market for the game. The developer collects scores from a random sample from each group. The results are shown below Group A Group B Group C 101 142 107 109 158 105 97 147 197 105 111 201 103 132 168 That is the mean sum of squares within  MS(Within)?
Jerry and a group of friends have decided to set up an online game night for...
Jerry and a group of friends have decided to set up an online game night for this Wednesday. Most of the games they will play involve a standard deck of playing cards (52 card deck). As such, Jerry hopes to use what he's learning in statistics class to gain an upper hand. **For reference, a standard deck of playing cards consists of 52 cards. Each card is one of the 4 suits: spade, heart, diamond, or club. Each suit contains...
You are testing the change in test scores following an intensive tutoring session. You have the...
You are testing the change in test scores following an intensive tutoring session. You have the following data from a small group of students each student is tested before and after the tutoring session. Each row represents one student. |Time 1 |Time 2| |---------|------| |65 |77 | |87 |100 | |77 |75 | |90 |89 | |70 |80 | |84 |81 | |92 |91 | |83 |96 | |85 |84 | |91 |89 | |68 |88 | |72 |100 |...
A national soccer team scores 1 goal per game on average. Let the data from the...
A national soccer team scores 1 goal per game on average. Let the data from the past 20 games be given by 1,2,2,1,1,1,1,2,1,4,0,2,3,0,2,1,0,3,4,1. Using this information, please answer the following questions. (a) (1 point) What is an appropriate statistical model for the number of goals scored in a given game if modeled by a random variable X taking values in {0, 1, 2, . . .}? (b) (1 point) Formulate an appropriate two-sided testing problem for the model’s parameter in...
Online shoppers have high expectations. Shoppers expect more from online shopping than easy-to-use websites. Successful online...
Online shoppers have high expectations. Shoppers expect more from online shopping than easy-to-use websites. Successful online retailers are creating online shopping experiences that encourage repeat customers and reward shopper loyalty. In 2013, UPS (United Parcel Service, Inc., Sandy Springs, GA) conducted a series of studies to gain insight about the shopping behavior of customers. The studies found that customers want to be able to shop anywhere at any time, and they want other services such as the flexibility to choose...
New drugs undergo preclinical and clinical testing.   Explain how preclinical and clinical testing differ from each...
New drugs undergo preclinical and clinical testing.   Explain how preclinical and clinical testing differ from each other and why preclinical testing is necessary
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT