The image shows a group of four individuals wearing graduation caps and gowns, standing on an open book.

According to the principal of a local high school, around 79% of their graduates who got admitted to a 4-year university do not complete their degree in 4 years. A class of 2020 had 150 graduates that got admitted to a 4-year university. Based on the data the principal expects that 21% of the class of 2020 will graduate by the end of 2024. Use the normal approximation along with the continuity correction factor to find the probability that at least 28 HS graduates from the class of 2020 will complete their degree by the end of 2024.
  • Let X\displaystyle {X} be the number of graduates in the class of 2020 that complete their degree by the end of 2024. Describe the distribution of X\displaystyle {X} and its parameters:

 X∼\displaystyle {X}\sim  ( n=\displaystyle {n}= , p=\displaystyle {p}= )

  • Use the random variable notation to symbolically express the probability that at least 28 graduates in the class of 2020 complete their degree by the end of 2024:

  • Let Y\displaystyle {Y} be a normal variable that will be used to approximate the probability in question. Find the parameters of Y\displaystyle {Y} (round the answers to 2 decimal places):

 Y∼\displaystyle {Y}\sim ( μ=\displaystyle \mu= , σ=\displaystyle \sigma= )

  • Use the random variable notation to symbolically express the approximate probability that at least 28 graduates in the class of 2020 complete their degree by the end of 2024:

  • Use the correction for continuity:

  • Find the probability (round the answer to 4 decimal places):

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