ice are man strength of the bag is normally distributed with a mean of 5 pounds
ID: 3365075 • Letter: I
Question
ice are man strength of the bag is normally distributed with a mean of 5 pounds per square inch and a standard deviation of 1.5 pounds per square inch. a. What proportion of the bags produced have a breaking strength of between5 and 5.5 pounds per square inch b. What proportion of the bags produced have a breaking strength of between 3.2 and 4.2 pounds per square inch. c. What proportion of the bags produced ha a breaking strength of at least 3.6 pounds per square inch. d. What proportion of the bags produced have a breaking strength of less than 3.17 pounds per square inch.Explanation / Answer
2.
NORMAL DISTRIBUTION
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 5
standard Deviation ( sd )= 1.5
a.
proportion of the bags produced have a breaking strenght of between 5 and 5.5 pounds per square inch
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 5) = (5-5)/1.5
= 0/1.5 = 0
= P ( Z <0) From Standard Normal Table
= 0.5
P(X < 5.5) = (5.5-5)/1.5
= 0.5/1.5 = 0.3333
= P ( Z <0.3333) From Standard Normal Table
= 0.6306
P(5 < X < 5.5) = 0.6306-0.5 = 0.1306
b.proportion of the bags produced have a breaking strenght of between 3.2 and 4.2 pounds per square inch
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 3.2) = (3.2-5)/1.5
= -1.8/1.5 = -1.2
= P ( Z <-1.2) From Standard Normal Table
= 0.1151
P(X < 4.2) = (4.2-5)/1.5
= -0.8/1.5 = -0.5333
= P ( Z <-0.5333) From Standard Normal Table
= 0.2969
P(3.2 < X < 4.2) = 0.2969-0.1151 = 0.1818
c.proportion of the bags produced have a breaking strenght of atleast 3.6 pounds per square inch
P(X < 3.6) = (3.6-5)/1.5
= -1.4/1.5= -0.9333
= P ( Z <-0.9333) From Standard Normal Table
= 0.1753
P(X > = 3.6) = (1 - P(X < 3.6)
= 1 - 0.1753 = 0.8247
d.proportion of the bags produced have a breaking strenght of less than 3.17 pounds per square inch
P(X < 3.17) = (3.17-5)/1.5
= -1.83/1.5= -1.22
= P ( Z <-1.22) From Standard Normal Table
= 0.1112
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