Answer:
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is differentiable across its domain, so the MVT says there is some value of

in the open interval

such that

You have

so the equation above becomes

Solve for

.




so

is indeed the average of the endpoints, i.e. the midpoint.
Answer:
x = 61, y = 29
Step-by-step explanation:
29+x = 90
x = 61
x + y = 90
y + 61 = 90
y = 29
Answer:
0.0039 is the probability that the sample mean hardness for a random sample of 12 pins is at least 51.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 50
Standard Deviation, σ = 1.3
Sample size, n = 12
We are given that the distribution of hardness of pins is a bell shaped distribution that is a normal distribution.
Formula:
Standard error due to sampling =

P(sample mean hardness for a random sample of 12 pins is at least 51)
Calculation the value from standard normal z table, we have,
0.0039 is the probability that the sample mean hardness for a random sample of 12 pins is at least 51.