Answer:

Step-by-step explanation:
Given

Required
Find a
Take log of both sides

Apply law of logarithm

Divide both sides by a

Multiply both sides by -9

Apply law of logarithm

Cancel out log

Rewrite as:

Apply law of indices


You would put 4-1 over 4-1 so the slope would be 3/3 which is one
so slope=1
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.