Normal Distribution: Practice 1.7 2008/06/17 13:59:24 GMT-5 2008/08/15 12:02:00.712 GMT-5 Barbara Illowsky illowskybarbara@deanza.edu Susan Dean deansusan@deanza.edu Connexions cnx@cnx.org elementary statistics

Student Learning Outcomes The student will explore the properties of data with 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. a Sketch the situation. Label and scale the axes. Shade the region corresponding to the probability.

b P ( 0 < X < _________ ) = _________ size 12{P \( 0<X<"_________" \) ="_________"} {} b 3,0 . 1979 size 12{3,0 "." "1979"} {} 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.

b P ( _______ < X < _______ ) = _________ size 12{P \( "_______"<X<"_______" \) ="_________"} {} b 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. a Sketch the situation. Label and scale the axes. Shade the region corresponding to the lower 70%.

b P(X<k)=_________ size 12{P \( X<k \) ="_________"} {}. Therefore, k=__________ size 12{k="__________"} {}. b 0.70,4.78 size 12{0 "." "70",4 "." "78"} {}years