Respuesta :
Answer:
a) 0.997 is the probability that the breaking strength is at least 772 newtons.
b) 0.974 is the probability that this material has a breaking strength of at least 772 but not more than 820
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 800 newtons
Standard Deviation, σ = 10 newtons
We are given that the distribution of breaking strength is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
a) P( breaking strength of at least 772 newtons)
[tex]P(x \geq 772)[/tex]
[tex]P( x \geq 772) = P( z \geq \displaystyle\frac{772 - 800}{10}) = P(z \geq -2.8)[/tex]
[tex]= 1 - P(z <-2.81)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x \geq 772) = 1 - 0.003 = 0.997 = 99.7\%[/tex]
0.997 is the probability that the breaking strength is at least 772 newtons.
b) P( breaking strength of at least 772 but not more than 820)
[tex]P(772 \leq x \leq 820) = P(\displaystyle\frac{772 - 800}{10} \leq z \leq \displaystyle\frac{820-800}{10}) = P(-2.8 \leq z \leq 2)\\\\= P(z \leq 2) - P(z < -2.8)\\= 0.977 - 0.003 = 0.974 = 97.4\%[/tex]
[tex]P(772 \leq x \leq 820) = 97.4\\%[/tex]
0.974 is the probability that this material has a breaking strength of at least 772 but not more than 820.
