Answer :
Answer: 0.1587
Step-by-step explanation:
Given : The foreman of a bottling plant has observed that the amount of soda in each 16-ounce bottle is actually a normally distributed random variable, with
[tex]\mu=15.9\text{ ounces}[/tex]
Standard deviation : [tex]\sigma=0.1\text{ ounce}[/tex]
Let x be the amount of soda in a randomly selected bottle.
Z-score : [tex]\dfrac{x-\mu}{\sigma}[/tex]
[tex]z=\dfrac{16-15.9}{0.1}=1[/tex]
The probability that the bottle will contain more than 16 ounces using standardized normal distribution table :
[tex]P(x>16)=P(z>1)=1-P(z<1)\\\\=1-0.8413447=0.1586553\approx0.1587[/tex]
Hence, the probability that the bottle will contain more than 16 = 0.1587