(Solved): Statistics  10. The table below is a probability of distribution where \( \mathrm{x} \) is the ...

10. The table below is a probability of distribution where \( \mathrm{x} \) is the number of people in a randomly selected group of 4 that recognizes the Sony brand of electronics. ( 6 pts) Math 1740 Take-Home Worksheet #1 Name: Shukri Haret You may use your books, notes, and Stat Crunch when necessary, but please be sure that your work is your own. 1) What is the probability that exactly 2 people in a group of 4 recognize the Sony brand? \( 0.1792 \) b) What is the probability that at least 2 people in a group of 4 recognize the Sony brand? c) What is the mean (expected value) for the number of people in group of 4 that recognize the Sony brand? (round to two decimal places). 11. A survey done by Nickelodeon found that \( 71 \% \) of kids living in Germany recognize the cartoon character SpongeBob. (10 pts) a) What is the probability that one randomly selected kid in Germany recognizes SpongeBob? b) What is the probability that one randomly selected kid in Germany does not recognize SpongeBob? c) Suppose we randomly selected a group of 5 children. What is the probability that exactly 3 of the 5 children recognize SpongeBob?