Question 596348: This is a Normal Probability Distribution problem. Can I get some step by step help in solving this problem so I can try solving the other problems by myself. I am really having a hard time. Thank you so much.
The weights of the contents of cans of tomato sauce produced by a company are normally distributed with a mean of 8 ounces and a standard deviation of 0.2 ounces.
a. What percentage of all cans produced contain more than 8.4 ounces of tomato paste?
b. What percentage of all cans produced contain less than 7.8 ounces?
c. What percentage of cans contains between 7.4 and 8.2 ounces?
d. Ninety-five percent of cans will contain at least how many ounces?
e. What percentage of cans contains between 8.2 and 8.4 ounces?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The weights of the contents of cans of tomato sauce produced by a company are normally distributed with a mean of 8 ounces and a standard deviation of 0.2 ounces.
-----
The measurement rod you must used is the z-distribution.
-------------------------
a. What percentage of all cans produced contain more than 8.4 ounces of tomato paste?
z(8.4) = (8.4-8)/0.2 = 0.4/0.2 = 2
P(x > 8.4) = P(z > 2) = normalcdf(2,100) = 0.0228
==============================================================
b. What percentage of all cans produced contain less than 7.8 ounces?
z(7.8) = (7.8-8)/0.2 = -1
P(x < 7.8) = P(z < -1) = normalcdf(-100,-1) = 0.1587
==============================================================
c. What percentage of cans contains between 7.4 and 8.2 ounces?
z(7.4) = (7.4-8)/0.2 = -3
z(8.2) = (8.2-8)/0.2 = 1
P(7.4< x <8.2) = P(-3< z <-1) = normcdf(-3,-1) = 0.1573
==============================================================
d. Ninety-five percent of cans will contain at least how many ounces?
Find the z-value with a left-tail of 0.95:
invNorm(0.95) = 1.645
Find the corresponding "x" value:
x = zs+u
x = 1.645*0.2+8 = 8.3290
=========================================
e. What percentage of cans contains between 8.2 and 8.4 ounces?
Using my TI-84: normalcdf(8.2,8.4,8,0.2) = 0.1359
=========================================
Cheers,
Stan H.
====================
|
|
|
