Answer:
a) Find the probability that the drink is less than 11.9 fluid ounces
We are supposed to find P(x<11.9)
x= 11.9
We will use z score formula :
Refer the z table
So, P(z<-0.67) = 0.2514
Hence the probability that the drink is less than 11.9 fluid ounces is 0.2514
b)Find the probability that the drink is between 11.6 and 11.9 fluid ounces
x= 11.6
We will use z score formula :
x= 11.9
We will use z score formula :
We are supposed to find P(11.6<x<11.9)
So, P(11.6<x<11.9)= P(x<11.9)-P(x<11.6)
P(-1.67<z<-0.67)= P(z<-0.67)-P(z<-1.67)
Refer the z table
P(-1.67<z<-0.67)= P(z<-0.67)-P(z<-1.67)
P(-1.67<z<-0.67)= 0.2514-0.0475
P(-1.67<z<-0.67)= 0.2039
So, the probability that the drink is between 11.6 and 11.9 fluid ounces is 0.2039.
c)Find the probability that the drink is more than 12.6 fluid ounces
We are supposed to find P(x>12.6)
x= 12.6
We will use z score formula :
Refer the z table
P(x>12.6)=1-P(x<12.6)
P(z>1.67)=1-P(z<1.67)
P(z>1.67)=1-0.9525
P(z>1.67)=0.0475
Hence the probability that the drink is more than 12.6 fluid ounces is 0.0475
d) Is the drink containing more than 12.6 fluid ounces an unusual event?
Since p value is less than alpha (0.05)
Answer = No, because the probability that a drink containing more than 12.6 fluid ounces is less than 0.05, this event is not unusual.