Respuesta :
Answer:
The diameters below 0.41 inches and above 0.89 inches are considered as defective.
Step-by-step explanation:
Let X = diameters of computer parts.
The random variable X is normally distributed with mean, μ = 6.5 inches and standard deviation, σ = 0.24 inches.
The pth percentile is a data value such that at least p% of the data set is less than or equal to this data value and at least (100 - p)% of the data set are more than or equal to this data value.
Compute the 16th percentile of X as follows:
P (X < x) = 0.16
⇒ P (Z < z) = 0.16
The value of z for this probability is:
z = -0.99
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\-0.99=\frac{x-6.5}{0.24}\\\\x=0.65-(0.99\times 0.24)\\\\x=0.4124\\\\x\approx 0.41[/tex]
The value at the 16th percentile is 0.44 inches.
Compute the 84th percentile of X as follows:
P (X < x) = 0.84
⇒ P (Z < z) = 0.84
The value of z for this probability is:
z = 0.99
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\0.99=\frac{x-6.5}{0.24}\\\\x=0.65+(0.99\times 0.24)\\\\x=0.8876\\\\x\approx 0.89[/tex]
The value at the 84th percentile is 0.89 inches.
Thus, the diameters below 0.41 inches and above 0.89 inches are considered as defective.
