Question

querstions A, B and C

1. A company is developing a mobile fitness app for their new activity tracker wristbands. The company wants to test the fitness app's accuracy in tracking the amount of non-sedentary activity as measured by their wristbands. A number of participants were recruited and divided into four different groups according to the level of self-reported fitness activity. Two locations were used to recruit participants. The following table shows the average group fitness scores for each group of participants in each recruitment location. Test Group Participants Group Fitness Score San Francisco: Group 1 1,515 255 San Francisco: Group 2 26 218 San Francisco: Group 3 3,290 317 San Francisco: Group 4 280 267 Los Angeles: Group 1 1,343 255 Los Angeles: Group 2 887 267 36 217 Los Angeles: Group 3 Los Angeles: Group 4 231 349 7.726 W Total o ni 2,027 a) Calculate the probability mass function of the Group Fitness Score (X) from the table b) Determine the cumulative distribution function for X c) According to these results, what is the probability that a new group of participants obtains a Group Fitness Score between 231 and 267? olvab olla ige d o lorib sobre la

Answer 1

a) To aim is to find the probability mass function to that data set The probability mass function is that X values corresponding to their respective probabilities The probabilities are computed to each Score (X) values by dividing each X value with the total of X values. This is 2027 Therefore, the probability mass function is shown below Participants f) Fitness score (X) Probabilities 255 0.1258 255 1515 2027 218 =0.10755 218 26 2027 317 = 0.15639 317 2027 3290 267 = 0.13172 267 280 2027 255 0.1258 255 1343 2027 267 = 0.13172 2027 267 887 217 = 0.10705 217 36 2027 231 = 0.11396 231 349 2027 Total: 2027 7726 1

b) The cumulative distribution function is obtained by adding up frequencies up to the respective score value Fitness score Participants( Probabilities Cumulative function (X) 255 0.1258 0.1258 1515 0.1075 0.1258+0.1075- 0.2333 26 218 0.1564 0.2333+0.1564 0.3897 317 3290 0.1317 0.3897+0.1317 0.5215 267 280 0.5215+ 0.1258 0.6473 0.1258 255 1343 0.1317 0.6473+0.1317 0.7790 267 887 0.1071 0.7790+0.1071 0.8860 217 36 0.1140 0.8860+0.1140 1.0000 349 231 Total-2027 7726

C) The total number of groups are 8 The groups that are between 231 and 267 are 5 Therefore, the required probability is, Number of groups that are between 231 and 267 P(231 Score 267) Total number of groups 5 8 0.625 Hence, the required probability is 0.625.