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Answer:
Two diameters that separate the top 4% and the bottom 4% are 5.77 and 5.53 respectively.
Step-by-step explanation:
We are given that the diameters of bolts produced in a machine shop are normally distributed with a mean of 5.65 millimeters and a standard deviation of 0.07 millimeters.
<em>Let X = diameters of bolts produced in a machine shop</em>
So, X ~ N()
The z score probability distribution is given by;
Z = ~ N(0,1)
where, = population mean
= standard deviation
<u>Now, we have to find the two diameters that separate the top 4% and the bottom 4%.</u>
- Firstly, Probability that the diameter separate the top 4% is given by;
P(X > x) = 0.04
P( >
) = 0.04
P(Z > ) = 0.04
<em>So, the critical value of x in z table which separate the top 4% is given as 1.7507, which means;</em>
= 1.7507
= 5.65 + 0.122549 = 5.77
- Secondly, Probability that the diameter separate the bottom 4% is given by;
P(X < x) = 0.04
P( <
) = 0.04
P(Z < ) = 0.04
<em>So, the critical value of x in z table which separate the bottom 4% is given as -1.7507, which means;</em>
= -1.7507
= 5.65 - 0.122549 = 5.53
Therefore, the two diameters that separate the top 4% and the bottom 4% are 5.77 and 5.53 respectively.