Respuesta :
Answer:
0.0039 is the probability that the sample mean hardness for a random sample of 12 pins is at least 51.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 50
Standard Deviation, σ = 1.3
Sample size, n = 12
We are given that the distribution of hardness of pins is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
Standard error due to sampling =
[tex]=\dfrac{\sigma}{\sqrt{n}} = \dfrac{1.3}{\sqrt{12}} = 0.3753[/tex]
P(sample mean hardness for a random sample of 12 pins is at least 51)
[tex]P( x \geq 51) = P( z \geq \displaystyle\frac{51 - 50}{0.3753}) = P(z \geq 2.6645)[/tex]
[tex]= 1 - P(z < 2.6645)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x \geq 51) = 1 - 0.9961= 0.0039[/tex]
0.0039 is the probability that the sample mean hardness for a random sample of 12 pins is at least 51.
