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Advocard [28]
2 years ago
6

An English professor assigns letter grades on a test according to the following scheme. A: Top 9% of scores B: Scores below the

top 9% and above the bottom 61% C: Scores below the top 39% and above the bottom 25% D: Scores below the top 75% and above the bottom 10% F: Bottom 10% of scores Scores on the test are normally distributed with a mean of 72.3 and a standard deviation of 8. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.
Mathematics
1 answer:
sergeinik [125]2 years ago
5 0

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 \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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 \mu = 72.3, \sigma = 8

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.

Z = \frac{X - \mu}{\sigma}

1.34 = \frac{X - 72.3}{8}

X - 72.3 = 1.34*8

X = 83

The minimum score required for an A grade is 83.

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An element with mass 490 grams decays by 28.6% per minute. How much of the element is remaining after 16 minutes, to the nearest
agasfer [191]

Answer:

2.2 grams

Step-by-step explanation:

We can use the compound decay formula shown below to solve this:

F=P(1-r)^t

Where

F is the final amount (what we want to find)

P is the present amount (490 grams)

r is the rate of decay, in decimal (28.6% = 28.6/100 = 0.286)

t is the time in minutes (16)

Substituting, we get:

F=P(1-r)^t\\F=490(1-0.286)^{16}\\F=490(0.714)^{16}\\F=2.2355

So, after 16 minutes, 2.2355 grams will be remaining.

<em>Rounded to nearest tenth of a gram (1 decimal place) = </em><em>2.2 grams remaining</em>

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3 years ago
Hillary leaves Point A traveling due east at a constant speed of 40 miles per hour. After Hillary has driven 22 miles, her broth
Marrrta [24]
51 miles per hour is the answer :)
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3 years ago
A class’s test scores are normally distributed if the average score 60 and the standard deviation is 7 choose the spots where th
Brrunno [24]

Answer:

46

Step-by-step explanation:

We are given that a  class's test scores are normally distributed with an average score of 60.

We know that the curve of a normal distribution is symmetric about its mean.

60-14=46

60+14=74

Hence, the point 46 lies to the left of the mean and 74 lies to the right of the mean, and the two points have the same function value.

5 0
2 years ago
Read 2 more answers
How many hours would someone earns 7.50 per hour have to work to earn $116.25
SCORPION-xisa [38]

Let h = amount of hours

7.5h=116.25

Since they earn $7.50 per hour, we can multiply that by an unknown amount of hours to get $116.25. Let's solve:

7.5h=116.25

Divide both sides by 7.5 to isolate the h, amount of hours.

\frac{7.5h}{7.5}=\frac{116.25}{7.5}

Simplify.

h=15.5

In conclusion, someone would have to work 15.5 hours to earn $116.25 if they earn $7.50 per hour.

5 0
3 years ago
If there is 520 grams of radioactive material with a half-life of 12 hours, how much of the radioactive material will be left af
AURORKA [14]
This is a fairly easy half-life problem
Each half-life reduces the radioactive material by one half.
So after 72 hours the radioactive material would have undergone 6 half-lives. 
2^6 = 64.
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520 / 64 = 8.125 grams will remain.
radioactive decay is an exponential decay function.

Source:
http://www.1728.org/halflife.htm


3 0
2 years ago
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