Answer:
0.0043 is the probability that the sample of 20 bottles have a mean below 19.90 fl oz.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 20 fl oz
Standard Deviation, σ = 0.17 fl oz
We are given that the distribution of amount of soft drink poured is a bell shaped distribution that is a normal distribution.
Sample size, n = 20
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
a) P(Sample of 20 bottles have a mean below 19.90 fl oz)
P(x < 19.90)
[tex]P( x < 19.90) = P( z < \displaystyle\frac{19.90-20}{\frac{0.17}{\sqrt{20}}}) = P(z < -2.6306)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x < 19.90) =0.0043= 0.43\%[/tex]
0.0043 is the probability that the sample of 20 bottles have a mean below 19.90 fl oz.