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5.9 Practice: the normal distribution

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Student learning outcomes

  • The student will analyze data following a normal distribution.

Given

The life of Sunshine CD players is normally distributed with a mean of 4.1 years and a standard deviation of 1.3 years. A CD player is guaranteed for 3 years. We are interested in the length of time a CD player lasts.

Normal distribution

Define the Random Variable X size 12{X} {} in words. X = size 12{X={}} {}

X ~

Find the probability that a CD player will break down during the guarantee period.

  • Sketch the situation. Label and scale the axes. Shade the region corresponding to the probability.
    Empty normal distribution curve.
  • P ( 0 < x < _________ ) = _________ size 12{P \( 0<x<"_________" \) ="_________"} {} (Use zero (0) for the minimum value of x.)
  • 3,0 . 1979 size 12{3,0 "." "1979"} {}

Find the probability that a CD player will last between 2.8 and 6 years.

  • Sketch the situation. Label and scale the axes. Shade the region corresponding to the probability.
    Empty normal distribution curve.
  • P ( _______ < x < _______ ) = _________ size 12{P \( "_______"<X<"_______" \) ="_________"} {}
  • 2 . 8,6,0 . 7694 size 12{2 "." 8,6,0 "." "7694"} {}

Find the 70th percentile of the distribution for the time a CD player lasts.

  • Sketch the situation. Label and scale the axes. Shade the region corresponding to the lower 70%.
    Empty normal distribution curve.
  • P ( x < k ) = _________ size 12{P \( x<k \) ="_________"} {} . Therefore, k = __________ size 12{k="__________"} {} .
  • 0 . 70 , 4 . 78 size 12{0 "." "70",4 "." "78"} {} years
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Source:  OpenStax, Collaborative statistics (custom lecture version modified by t. short). OpenStax CNX. Jul 15, 2013 Download for free at http://cnx.org/content/col11543/1.1
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