Download HW #24 SD/Norm Dist WS standard_deviation

HW #24
Standard Deviation and Normal Distribution
Name ______________________________
For each problem, 1-5 below, draw a sketch of the normal distribution and shade the appropriate region of
the curve. Then determine the answer, showing all your work or calculations performed on the calculator.
Circle your final answer.
Lizzie (female) and Simba (male) are good friends who consider themselves tall for their gender. Simba
is 6’1” and Lizzie is 5’9” and both are full-grown adults. Obviously Simba is taller than Lizzie, but one
day they were arguing about who is taller relative to their gender. They looked up some data on the
internet that stated adult men in the US have an average height of 69 inches with a standard deviation of
3.25 inches and adult women have an average height of 64 inches with a standard deviation of 2.75
inches.
1. What percent of adult women have a height between 61.25 inches and 69.5 inches?
2. If an adult man were selected at random from the US population, what is the probability that he
would be taller than Simba?
3. There are 56,200 adult women in a certain town. Assuming these women’s heights are
representative of all US adult women, how many of these women would be shorter than Lizzie?
4. If “really, really tall” means that a person’s height is in the top 1% of his/her gender, how tall does
a man have to be in order to be considered really, really tall?
5. With the original statistics in mind, as well as your responses above, write an argument for
whether you think Simba or Lizzie is taller for his/her gender. Explain your answer
mathematically and using a sketch of a normal curve.