Answer:
Where
and 
Since the distribution for X is normal then the distribution for the sample mean is also normal and given by:



So then is appropiate use the normal distribution to find the probabilities for 
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean". The letter
is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: 
Solution to the problem
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
Where
and 
Since the distribution for X is normal then the distribution for the sample mean
is also normal and given by:



So then is appropiate use the normal distribution to find the probabilities for 
Answer:
47.13
Step-by-step explanation:
Circumfrence= 2 x pi x Radius
2 x 3.142 x 7.5 =47.13
For this answer, you multiply the weight of each penny nail by x and the weight of each wood nail by y. If the bag holds one pound of nails, you would use the inequality ≤.
.05x + 0.1y ≤ 1
C = 2pi r= 2 (3.14) (27) = 169.56
Let XY = x
169.56 / 360 = x / 60
360x = 169.56 * 60
360x = 10173.60
x = 28.26
x = 28.3
Answer is C. 28.3 cm