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5-82.

According to the National Health Statistics Report, the average height of adult women in the U.S. is inches with a standard deviation of inches. Heights can be modeled with a normal probability density function. Homework Help ✎

  1. According to this model, what percentage of women in the U.S. are under feet inches tall?

    First, note that feet 11 inches must be converted to inches.

    normalcdf

  2. Most girls reach their adult height by their senior year in high school. In North City High School’s senior class of students, how many girls would you predict are shorter than feet inches? (Note: Assume half of the senior students are girls.)

    Multiply by the percentage found in part (a).

  3. How many senior girls would you predict are taller than feet at North City High? What assumption(s) are you making?

    Follow the same steps you used in part (a).

  4. Suppose you find out that North City High School is a private boarding school with a championship girl’s basketball program, and they recruit basketball players from across the state. Would your answer to part (c) change? Explain.

    It is likely that there will be girls over feet tall, and the senior girls are probably not a representative sample of women in the U.S.