Answer:
a

b

Step-by-step explanation:
From the question we are told that
The mean value is 
The standard deviation is 
Considering question a
The sample size is n = 9
Generally the standard error of the mean is mathematically represented as

=>
=> 
Generally the probability that the sample mean hardness for a random sample of 9 pins is at least 51 is mathematically represented as



=> 
From the z table the area under the normal curve to the left corresponding to 2.5 is

=> 
=> 
Considering question b
The sample size is n = 40
Generally the standard error of the mean is mathematically represented as

=>
=> 
Generally the (approximate) probability that the sample mean hardness for a random sample of 40 pins is at least 51 is mathematically represented as

=> 
=> 
From the z table the area under the normal curve to the left corresponding to 5.2715 and
=> 
So

=> 
Answer:
Hi. I am a math teacher. Your correct answer is 210. You're welcome!
Answer:
y = - 2x -10
Step-by-step explanation:
y = -2x + 1 Slope , m = -2 parallel slope is the same
point slope form of new line
(y - -4)= -2 ( x - -3)
<u>y = -2x -10 </u>
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