Answer:
The mean of weight is 30.3
Step-by-step explanation:
We are given the following information in the question:
Standard Deviation, σ = 6 ounces
We are given that the weights is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(container holds less than 18 ounces) = 2% = 0.02
P(x < 18) = 0.02
[tex]P( x < 18) = P( z < \displaystyle\frac{18 - \mu}{6}) = 0.02[/tex]
Calculation the value from standard normal z table, we have,
P(Z < -2.05) = 0.02
[tex]\displaystyle\frac{18 - \mu}{6} = -2.05\\\\\mu =18- (6\times -2.05) = 30.3[/tex]
Hence, the mean of weight is 30.3
