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erastova [34]
3 years ago
11

The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring t

he depth of penetration of the point. Suppose the Rockwell hardness of a particular alloy is normally distributed with mean 68 and standard deviation 3. (Rockwell hardness is measured on a continuous scale).(A) If a specimen is acceptable only if its hardness is between 67 and 75, what is the probability that a randomly chosen specimen has an acceptable hardness?(B) If the acceptable range of hardness is (70-c, 70+c), for what value of c would 95% of all specimens have acceptable hardness?
Mathematics
1 answer:
adoni [48]3 years ago
7 0

Answer:

Step-by-step explanation:

Given that the Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point.

Let X be the hardness

X is N(68,3)

a) P(67

This area lies on both sides of the mean. Hence we add the corresponding prob values form table

= 0.1293+0.4901=0.6194

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The common ratio of a geometric series is 3 and the sum of the first 8 terms is 3280.
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Answer:

The first term of the geometric series is 1

Step-by-step explanation:

In this question, we are tasked with calculating the first term of a geometric series, given the common ratio, and the sum of the first 8 terms.

Mathematically, the sum of terms in a geometric series can be calculated as;

S = a(r^n-1)/( r-1)

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Plugging these values, we have

3280 = a(3^8 -1)/(3-1)

3280 = a( 6561-1)/2

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