Respuesta :
Answer:
a) 0.216
b) 0.1587
c) 0.369
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 12.2 grams
Standard Deviation, σ = 2.8 grams
We are given that the distribution of weights of impurities per bag is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
a) P(contains less than 10 grams of impurities)
P(x < 10)
[tex]P( x < 10) = P( z < \displaystyle\frac{10 - 12.2}{2.8}) = P(z < -0.7857)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x < 10) =0.216= 21.6\%[/tex]
b) P(contains more than 15 grams of impurities)
P(x > 15)
[tex]P( x > 15) = P( z > \displaystyle\frac{15 - 12.2}{2.8}) = P(z > 1)[/tex]
[tex]= 1 - P(z \leq 1)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x > 610) = 1 - 0.8413 = 0.1587 = 15.87\%[/tex]
c) P(contains between 12 and 15 grams of impurities)
[tex]P(12 \leq x \leq 15) = P(\displaystyle\frac{12 - 12.2}{2.8} \leq z \leq \displaystyle\frac{15-12.2}{2.8}) \\\\= P(-0.0714 \leq z \leq 1)\\\\= P(z \leq 1) - P(z < -0.0714)\\= 0.841 - 0.472 = 0.369 = 36.9\%[/tex]
[tex]P(12 \leq x \leq 15) = 36.9%[/tex]
d) The mean divide the data in exactly two parts. Since 15 is farther away from the mean as compared to 10, the probability obtained in part (b) is smaller as compared to probability obtained in part (a).
