# An analysis of the grades on the first test in History 101 revealed that they approximate a normal curve with a mean of 75 and a standard deviation of 8. The instructor wants to award the grade of A to the upper 10% of the test grades. To the nearest percent, what is the dividing point between an A and a B grade? Select one: a. 80 b. 85 c. 90 d. 95

b. 85

Step-by-step explanation:

Standard deviation (σ) = 8

Assuming a normal distribution, the z-score corresponding to the upper 10% of the test grades is z = 1.28.

The minimum grade 'X' within the top 10% is given by:

Rounding to the nearest percent, the dividing point between an A and a B grade is 85.

## Related Questions

Step-by-step explanation:

Quadrants 3 &4 represent negative integers. If 0 on the x axis represents the average/mean number of people there, then 3& 4 show the decrease from the average number.

Which expression equals 24?

Lots.

Step-by-step explanation:

12 + 12, 2 x 12, 48 divided 2, etc.

Lots of expressions make 24.

Answer:For this case we must find an expression equivalent to 24, including exponents. To do this, we decompose factor 24. By definition, factorial decomposition consists of writing a number as the multiplication of other numbers.

Then:

We have the "2" is written three times, then:

Answer:24 = 2 to the 3rd power x 3

Step-by-step explanation:

The Venn diagram shows the relationship betweenseveral sets of numbers.
Where should 0.3% be placed in the Venn diagram?
Real numbers
Natural numbers, because 0.3% is a positive
number
B
Integers, because 0.3% is a decimal
Integers
Rational
numbers
Natural
numbers
Rational numbers, because 0.3% can be
written as a fraction
Real numbers, because 0.3% is an irrational
number

Rational numbers, because 0.3% can be

written as a fraction

Step-by-step explanation:

Step-by-step explanation:

Paired t‐Test for Mean Comparison with Dependent Samples To study the effects of an advertising campaign at a supply chain, several stores are randomly selected with the following observed before‐ and after‐advertising monthly sales revenues: Store number 1 2 3 4 5
Old sales revenue (mil. $) 5.2 6.5 7.2 5.7 7.6 New sales revenue (mil.$) 6.4 7.8 6.8 6.5 8.2
Let μ₁ and μ₂ be the means of old and new sales revenues, both in millions of dollars per month.
(a) At α = 0.05, test H0: μ2 ≤ μ1 versus H1: μ2 > μ1. Sketch the test. Interpret your result.
(b)Sketch and find the p‐value of the test. Would you reject H0 if α = 0.01?

a)

So the p values is lower than the significance level given 0.05, so then we can conclude that we reject the null hypothesis.

b) The p value is illustrated on the figure attached.

If we select we see that so then we have enough evidence to FAIL to reject the null hypothesis.

Step-by-step explanation:

Part a

A paired t-test is used to compare two population means where you have two samples in  which observations in one sample can be paired with observations in the other sample. For example  if we have Before-and-after observations (This problem) we can use it.

Let put some notation

1=test value old , 2 = test value new

1: 5.2 6.5 7.2 5.7 7.6

2: 6.4 7.8 6.8 6.5 8.2

The system of hypothesis for this case are:

Null hypothesis:

Alternative hypothesis:

The first step is calculate the difference and we obtain this:

d: 1.2, 1.3, -0.4, 0.8, 0.6

The second step is calculate the mean difference

The third step would be calculate the standard deviation for the differences, and we got:

The 4 step is calculate the statistic given by :

The next step is calculate the degrees of freedom given by:

Now we can calculate the p value, since we have a right tailed test the p value is given by:

So the p values is lower than the significance level given 0.05, so then we can conclude that we reject the null hypothesis.

Part b

The p value is illustrated on the figure attached.

If we select we see that so then we have enough evidence to FAIL to reject the null hypothesis.

A company is considering a new manufacturing process. It knows that the rate of savings (in dollars per year) from the process will be about S(t) = 5000(t + 3), where t is the number of years the process has been in use. Find the total savings during the first year. Find the total savings during the first 5 years. The total savings during the first year is __________

Total saving during first 5 years=$137500 Total saving during first year=$17500

Step-by-step explanation:

We are given that

Savings rate

Total saving during first 5 years is given by

Total saving during first 5 years==$137500 Total saving during first year= Total saving during first year= Total saving during first year=$17500

Write a trinomial with 3x as the GCF of its terms.​