Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.2.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?b. Without assuming population normality, what is the (approximate) probability that the sample mean hardness for a random sample of 40 pins is at least 51?

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

=>

a. 74 degrees

step-by-step explanation:

because the lines through the side and the box in the corners shows that these are congruent triangles and since they are mirrored the 37 degrees is also mirrored so the answer is 37 * 2 which is 74.

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following