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Practice: The Normal Distribution

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

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

Exercise 1

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

Exercise 2

X X~

Exercise 3

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

  • a. Sketch the situation. Label and scale the axes. Shade the region corresponding to the probability.
    Figure 1
    Empty normal distribution curve.
  • b. P ( 0 < x < _________ ) = _________ P ( 0 < x < _________ ) = _________ size 12{P \( 0<x<"_________" \) ="_________"} {} (Use zero (0) for the minimum value of x.)

Solution

  • b. 3,0 . 1979 3,0 . 1979 size 12{3,0 "." "1979"} {}

Exercise 4

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

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

Solution

  • b. 2 . 8,6,0 . 7694 2 . 8,6,0 . 7694 size 12{2 "." 8,6,0 "." "7694"} {}

Exercise 5

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

  • a. Sketch the situation. Label and scale the axes. Shade the region corresponding to the lower 70%.
    Figure 3
    Empty normal distribution curve.
  • b. P(x<k)=_________P(x<k)=_________ size 12{P \( x<k \) ="_________"} {}. Therefore, k=__________k=__________ size 12{k="__________"} {}.

Solution

  • b. 0.70,4.780.70,4.78 size 12{0 "." "70",4 "." "78"} {}years

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