A study was made of 200 preschoolers to determine if they watched some particular television shows. The choices were Little Galileo, Super Reader and Prehistoric Train. The results are
I. 22 preschoolers did not watch any of these shows
II. 73 preschoolers only watched Little Galileo
III. 136 preschoolers watched Little Galileo
IV. 14 preschoolers only watched Super Reader and Prehistoric Train
V. 31 preschoolers only watched Little Galileo and Prehistoric Train
VI. 63 preschoolers watch Super Reader
VII. 135 preschoolers do not watch Prehistoric Train
Choose the following statements about the probabilities of preschool television viewing that are correct.
68% of the preschoolers watched Little Galileo
31.5% of preschoolers do NOT watch Super Reader
67.5% of preschoolers only watch Prehistoric Train.
89% of the preschoolers watch Little Galileo, Super Reader, or Prehistoric Train.
35.4% of preschoolers who watch a show watch Super Reader.
22% of preschoolers do NOT watch Little Galileo, Super Reader or Prehistoric Train.
7% of preschoolers only watch Prehistoric Train and Super Reader.
23.6% of preschoolers who watch a show watch Little Galileo.
68.5% of the preschoolers do NOT watch Super Reader
75.8% preschoolers who watch a show, do NOT watch Prehistoric Train.
www.jiskha.com/questions/1786137/A-study-was-made-of-200-preschoolers-to-determine-if-they-watched-some-particular
To answer the statements about the probabilities of preschool television viewing, we can use the information given in the study. Let's go through each statement and determine if it is correct or not:
1. 68% of the preschoolers watched Little Galileo: This statement is incorrect because the given information tells us that 136 preschoolers watched Little Galileo out of a total of 200 preschoolers. The proportion that watched Little Galileo is 136/200 = 0.68 or 68%, which is the correct answer.
2. 31.5% of preschoolers do NOT watch Super Reader: To find the percentage of preschoolers who do not watch Super Reader, we can subtract the number of preschoolers who watch Super Reader (63) from the total number of preschoolers (200), and then divide by the total number of preschoolers. (200 - 63)/200 = 0.685 or 68.5%. So, this statement is incorrect.
3. 67.5% of preschoolers only watch Prehistoric Train: To find the percentage of preschoolers who only watch Prehistoric Train, we add the number of preschoolers who only watch Prehistoric Train (31) to the number of preschoolers who watch both Little Galileo and Prehistoric Train (31), and then divide by the total number of preschoolers. (31 + 31)/200 = 0.31 or 31%. So, this statement is incorrect.
4. 89% of the preschoolers watch Little Galileo, Super Reader, or Prehistoric Train: To find the percentage of preschoolers who watch at least one of the three shows, we can add the number of preschoolers who watch each show separately (136 + 63 + 31) and divide by the total number of preschoolers. (136 + 63 + 31)/200 = 0.65 or 65%. So, this statement is incorrect.
5. 35.4% of preschoolers who watch a show watch Super Reader: To find the percentage of preschoolers who watch a show and also watch Super Reader, we divide the number of preschoolers who watch Super Reader (63) by the total number of preschoolers who watch a show (136 + 63 + 31). 63/(136 + 63 + 31) = 0.23 or 23%. So, this statement is incorrect.
6. 22% of preschoolers do NOT watch Little Galileo, Super Reader, or Prehistoric Train: To find the percentage of preschoolers who do not watch any of the three shows, we can use the information that 22 preschoolers did not watch any of these shows. So, 22/200 = 0.11 or 11%. Therefore, this statement is incorrect.
7. 7% of preschoolers only watch Prehistoric Train and Super Reader: To find the percentage of preschoolers who only watch Prehistoric Train and Super Reader, we can use the information that 14 preschoolers only watched Super Reader and Prehistoric Train. So, 14/200 = 0.07 or 7%. Therefore, this statement is correct.
8. 23.6% of preschoolers who watch a show watch Little Galileo: To find the percentage of preschoolers who watch a show and also watch Little Galileo, we divide the number of preschoolers who watch Little Galileo (136) by the total number of preschoolers who watch a show (136 + 63 + 31). 136/(136 + 63 + 31) = 0.56 or 56%. Therefore, this statement is incorrect.
9. 68.5% of the preschoolers do NOT watch Super Reader: To find the percentage of preschoolers who do not watch Super Reader, we can subtract the number of preschoolers who watch Super Reader (63) from the total number of preschoolers (200), and then divide by the total number of preschoolers. (200 - 63)/200 = 0.685 or 68.5%. So, this statement is correct.
10. 75.8% of the preschoolers who watch a show, do NOT watch Prehistoric Train: To find the percentage of preschoolers who watch a show and do not watch Prehistoric Train, we need to subtract the number of preschoolers who watch both Little Galileo and Prehistoric Train (31) from the total number of preschoolers who watch a show (136 + 63 + 31), and then divide by the total number of preschoolers who watch a show. (136 + 63)/(136 + 63 + 31) = 0.818 or 81.8%. So, this statement is incorrect.
To summarize, the correct statements about the probabilities of preschool television viewing are:
- 68% of the preschoolers watched Little Galileo.
- 7% of preschoolers only watch Prehistoric Train and Super Reader.
- 68.5% of the preschoolers do NOT watch Super Reader.