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rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.6. (round your answers to four decimal places.) a button hyperlink to the salt program that reads: use salt. (a) if the distribution is normal, what is the probability that the sample mean hardness for a random sample of 9 pins is at least 51? 0.0131 incorrect: your answer is incorrect. (b) what is the (approximate) probability that the sample mean hardness for a random sample of 41 pins is at least 51? 0.00 correct: your answer is correct.



Answer :

The Answer will be 0.0002 using standard deviation

What is standard deviation?

The standard deviation is a statistician's way of gauging how much a group of numbers can vary or be dispersed. The values tend to be close to the set's mean when the standard deviation is low, while the values are dispersed over a larger range when the standard deviation is high.

Here let n = 41 random sample.

The mean = 50

and standard deviation = 1.6

So the distribution will be 1.6/[tex]\sqrt{41}[/tex] = 0.254

probability that the sample mean hardness for a random sample of 41 pins is at least 51 is

p(x>51) = 1 - p(x<51)

=1- p(z - 1/254)

= 1 - p(z-3.84)

=1-.9998

=0.0002

Hence the probabilty is 0.0002

Learn more about standard deviation, by the following link.
https://brainly.com/question/475676
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