Respuesta :
Answer:
Option D) 7.90 g and 8.12 g
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 8.01 g
Standard Deviation, σ = 0.06 g
We are given that the distribution of weights is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
We have to find the value of x such that the probability is 0.03
P(X > x)
[tex]P( X > x) = P( z > \displaystyle\frac{x - 8.01}{0.06})=0.03[/tex]
[tex]= 1 -P( z \leq \displaystyle\frac{x - 8.01}{0.06})=0.03 [/tex]
[tex]=P( z \leq \displaystyle\frac{x - 8.01}{0.06})=0.97 [/tex]
Calculation the value from standard normal z table, we have,
[tex]\displaystyle\frac{x - 8.01}{0.06} = 1.881\\\\x = 8.12[/tex]
Thus, 8.17 g separates the top 3% of the weights.
P(X < x)
[tex]P( X < x) = P( z < \displaystyle\frac{x - 8.01}{0.06})=0.03[/tex]
Calculation the value from standard normal z table, we have,
[tex]\displaystyle\frac{x - 8.01}{0.06} = -1.881\\\\x = 7.90[/tex]
Thus, 7.90 separates the bottom 3% of the weights.
Thus, the correct answer is
Option D) 7.90 g and 8.12 g
