Respuesta :
Answer:
The probability that the sample mean would differ from the population mean by greater than 2.2 millimeters is 0.0222.
Step-by-step explanation:
Let X = the diameter of steel bolts.
The population mean diameter of steel bolts is, μ = 125 mm and the population variance is, σ² = 49 mm.
A random sample of n = 41 steel bolts are selected.
According to the Central limit theorem, if a large sample (n > 30) is selected from an unknown population with mean μ and variance σ² then the sampling distribution of sample mean follows a Normal distribution with mean, [tex]\mu_{\bar x}=\mu[/tex] and variance, [tex]\sigma_{\bar x}^{2}=\frac{\sigma^{2}}{n}[/tex].
Compute the probability that the sample mean differ from the population mean by greater than 2.2 mm as follows:
[tex]P(\bar X-\mu>2.2)=P(\frac{\bar X-\mu}{\sigma_{\bar x}}>\frac{2.2}{\sqrt{49/41}})\\=P(Z>2.01)\\=1-P(Z<2.01)\\=1-0.9778\\=0.0222[/tex]
*Use a z-table for the probability.
Thus, the probability that the sample mean would differ from the population mean by greater than 2.2 millimeters is 0.0222.
