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Collaborative statistics The normal distribution Practice: the normal distribution
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
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 \( 0<x<"_________" \) ="_________"} {} (Use zero (0) for the minimum value of x.)
b
3,0
.
1979
size 12{3,0 "." "1979"} {} Got questions? Get instant answers now!
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"} {} Got questions? Get instant answers now!
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 Got questions? Get instant answers now!
Source:
OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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