Question

1. water mineral bottle contained with volume 1 litre water following normal distribution with average 1 litre and standard deviation 0.04 litre. if bottle volume is less than 95% from valid standard volume (in this case 0.95 littre), company will get penalty from consumer foundation. bottle with volume above 1.1 litre will be spilled if opened.

a. how much bottle proportion with volume between 0.9 and 1.1 litre?
b. total chance the company will get penalty from consumer foundation?
c. total chance bottle that will be spilled when opened?
d. total at least botle sample contained in 99% air mineral bottle?

2. in case question (number 1) above taken from random 25 sample bottle
a. how much chance average for bottle volume between 0.95 and 1.1 litre
b. how much chance average for bottle volume for more than 1.1 litre
c. how much at least an average bottle volume sample if chance rate is 95%

NOTE: not using paper/handwritten answer is much appreciated. because it will hard for me to read the math symbol when its handwritten.

Answer 1

(there are more than 4 parts, as per policy i am answering first 4 parts, i.e , 1:a,b,c,d)

1.

P(z<Z) table :

a.

b.

c.

d.

for 99%

P(z>=Z) = 0.99

P(z<Z) = 1-0.99 = 0.01

Z (from table) = -2.33

content = mean + z*SD

= 1 - 2.33*0.04

= 0.9068 litre

(please UPVOTE)