A perfume bottle is designed to have a capacity of 15 ounces. There is variation

Question

A perfume bottle is designed to have a capacity of 15 ounces. There is variation in the bottle manufacturing process. Based on historical data, it is believed that the bottle capacity can be reasonably modeled by a normal distribution with a mean of 15 ounces and a standard deviation of 0.1 ounces.

A) In a run of 100,000 of these bottles, how many will have a capacity between 14.8 and 15.15 ounces?

** Please make sure you include the calculations, formulas, and any explaination on how to do this problem. Just showing I answer I can't figure out how to do the problem properly. Here are the questions.

Explanation / Answer

Mean ( u ) =15
Standard Deviation ( sd )=0.1
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 14.8) = (14.8-15)/0.1
= -0.2/0.1 = -2
= P ( Z <-2) From Standard Normal Table
= 0.02275
P(X < 15.15) = (15.15-15)/0.1
= 0.15/0.1 = 1.5
= P ( Z <1.5) From Standard Normal Table
= 0.93319
P(14.8 < X < 15.15) = 0.93319-0.02275 = 0.9104                  

the percentage of b/w 14.8 to 15.15 is 91.04
& the number of bottles in a run of 100,000 is 0.9104 * 100000 is 91040

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