The manufacturer of a coffee dispensing machine claims the o

The manufacturer of a coffee dispensing machine claims the ounces per cup is mound-shaped and symmetric with mean u= 7 ounces and standard deviation o= 0.8 ounce. If 40 cups of coffee are measured, what is the probability the average ounces per cup x is:

a. u-x= and o-x=

b. less than 6.8 ounces? P( ) = P( ) = _______________

c. more than 7.4 ounces? P( ) = P( ) = _______________

d. between 6.8 and 7.4 ounces? P( ) = P( ) = _______________

Solution

a)
Mean ( u ) =7
Standard Deviation ( sd )=0.8/ Sqrt ( 40 ) = 0.1265
Number ( n ) = 40
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
a)
P(X < 6.8) = (6.8-7)/0.8/ Sqrt ( 40 )
= -0.2/0.1265= -1.5811
= P ( Z <-1.5811) From Standard NOrmal Table
= 0.0569                  
b)
P(X > 7.4) = (7.4-7)/0.8/ Sqrt ( 40 )
= 0.4/0.126= 3.1623
= P ( Z >3.1623) From Standard Normal Table
= 0.0008                  
c)
To find P(a <= Z <=b) = F(b) - F(a)
P(X < 6.8) = (6.8-7)/0.8/ Sqrt ( 40 )
= -0.2/0.1265
= -1.5811
= P ( Z <-1.5811) From Standard Normal Table
= 0.05692
P(X < 7.4) = (7.4-7)/0.8/ Sqrt ( 40 )
= 0.4/0.1265 = 3.1623
= P ( Z <3.1623) From Standard Normal Table
= 0.99922
P(6.8 < X < 7.4) = 0.99922-0.05692 = 0.9423