Answer:
The minimum score required for an A grade is 83.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean 
and standard deviation 
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 72.3 and a standard deviation of 8.
This means that 
Find the minimum score required for an A grade.
This is the 100 - 9 = 91th percentile, which is X when Z has a pvalue of 0.91, so X when Z = 1.34.
The minimum score required for an A grade is 83.
Employ a standard trick used in proving the chain rule:
The limit of a product is the product of limits, i.e. we can write
The rightmost limit is an exercise in differentiating
using the definition, which you probably already know is
.
For the leftmost limit, we make a substitution
. Now, if we make a slight change to
by adding a small number
, this propagates a similar small change in
that we'll call
, so that we can set
. Then as
, we see that it's also the case that
(since we fix
). So we can write the remaining limit as
which in turn is the derivative of
, another limit you probably already know how to compute. We'd end up with
, or
.
So we find that
Answer:
D. There is not enough information to make a conclusion about the population mean.
Step-by-step explanation:
One of the crafters Chris has a sample means of 200. This means that the average amount of yarn Chris used is 200 meters. Yet there is nothing else given about the other crafters, hence it is impossible to draw a conclusion.
