9 facebook friends based on a study of us facebook

This preview shows page 6 - 8 out of 8 pages.

9. Facebook Friends: Based on a study of U.S. Facebook users in 2014, the most connected age group were Facebook users between 18 and 24 years, averaging 649 friends on the social media website. Assume the distribution for the number of Facebook friends for this age group is approximately normal with mean of 649 friends and a standard deviation of 150 friends. a. Based on the model, determine the value that would correctly complete the sentence below. [2]
Using the z table we find that a z score = 1.04 has an area to the left of 0.8500. So we need to solve for the number of friends: 𝟏𝟏 . 𝟎𝟎𝟒𝟒 = 𝒙𝒙−𝟔𝟔𝟒𝟒𝟔𝟔 𝟏𝟏𝟓𝟓𝟎𝟎 , x = 649 + 1.04(150) = 802 Note: If they use z = 1.05 and get 803.5 it is ok. Final Answer: at least ______ 802 ______ friends b. Based on the model, what is the probability that a randomly selected Facebook user between 18 to 24 years has at least 844 friends? [2]
c. Consider a random sample of 8 Facebook users between 18 to 24 years. What is the probability that exactly 3 of the 8 Facebook users will have at least 844 friends? [3]
Stats 250 Fall 2016 Exam 1 Page 6 of 7 10. Abandoning Landlines: The Centers for Disease Control and Prevention reported that 41% of all U.S. households use only cellphones (no landlines). Suppose this rate is indeed correct. A random sample of 60 U.S. households will be selected, and the sample proportion that use only cellphones will be computed. a. In order to understand if finding at least 50% of the sampled households use only cellphones would be unusual, having a frame of reference would be helpful. Provide that frame of reference by giving a complete sketch of the approximate distribution of the possible values for such a sample proportion . Include a label for the x axis, a complete label for the distribution, and, using the empirical rule, provide at least three values along the x axis. [3] b. Compute the approximate probability that at least 50% of the sampled households use only cellphones. [3] Using the approximate normal model for a sample proportion N(0.41, (. 𝟒𝟒𝟏𝟏 )( 𝟏𝟏− . 𝟒𝟒𝟏𝟏 )/ 𝟔𝟔𝟎𝟎 ) or N(0.41 , 0.0635) distribution. So we need to standardize: 𝒛𝒛 = 𝟎𝟎 . 𝟓𝟓𝟎𝟎−𝟎𝟎 . 𝟒𝟒𝟏𝟏 𝟎𝟎 . 𝟎𝟎𝟔𝟔𝟑𝟑𝟓𝟓 = 1.42, and the area to the right of z = 1.42 is found from z table as 1 – 0.9222 = 0.0778. Final Answer: _____ 0.0778 _____ 11. Reading Habits After High School: A recent publication in Time magazine reported that 70% of high school graduates read a book in the summer after graduation. The principal of Pioneer High School (PHS) asks the AP statistics teacher to conduct a study to assess whether more than 70% of PHS graduates read a book in the summer after graduation. The teacher will contact a random sample of 25 recent PHS graduates and record

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture