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PilotLPTM [1.2K]
3 years ago
10

On a quiz worth 5 points, four students earned a 5, seven students earned a 4, six students earned a 3, two students earned a 2,

and one student earned a zero. Find the average score. (round to the tenths place)
Mathematics
1 answer:
Keith_Richards [23]3 years ago
5 0

Answer:

The average score is 3.5.

Step-by-step explanation:

The average of a data set is the middle value or the most typical value of the set. It computed by dividing the sum of observations by the number of observations.

The sample space of the scores are:

S = {5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 2, 2, 0}

Total number of students = 4 +7 + 6 + 2 + 1 = 20.

The average score is:

Average=\frac{1}{n}\sum x\\=\frac{1}{20}(5+5+5+5+4+4+4+4+4+4+4+3+3+3+3+3+3+2+2+0)\\=\frac{70}{20} \\=3.5

Thus, the average score is 3.5.

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The scores on the GMAT entrance exam at an MBA program in the Central Valley of California are normally distributed with a mean
Kaylis [27]

Answer:

58.32% probability that a randomly selected application will report a GMAT score of less than 600

93.51%  probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600

98.38% probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

\mu = 591, \sigma = 42

What is the probability that a randomly selected application will report a GMAT score of less than 600?

This is the pvalue of Z when X = 600. So

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

Z = \frac{600 - 591}{42}

Z = 0.21

Z = 0.21 has a pvalue of 0.5832

58.32% probability that a randomly selected application will report a GMAT score of less than 600

What is the probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600?

Now we have n = 50, s = \frac{42}{\sqrt{50}} = 5.94

This is the pvalue of Z when X = 600. So

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

Z = \frac{600 - 591}{5.94}

Z = 1.515

Z = 1.515 has a pvalue of 0.9351

93.51%  probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600

What is the probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600?

Now we have n = 50, s = \frac{42}{\sqrt{100}} = 4.2

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

Z = \frac{600 - 591}{4.2}

Z = 2.14

Z = 2.14 has a pvalue of 0.9838

98.38% probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600

8 0
3 years ago
You work as a quality control inspector of shirts for a clothing manufacturing company. Today you examine one batch and 15% fail
Otrada [13]

Answer:

23%

Step-by-step explanation:

To find how many failed inspection, add together all the percentages:

15 + 5 + 3

= 23

So, 23% of the products failed inspection

5 0
2 years ago
How do you calculate the volume of a liquid? How do you calculate the volume of a liquid? 1 following 6 answers 6 Report Abuse A
Nana76 [90]
Hello there.

<span>How do you calculate the volume of a liquid? 

</span>To measure<span> the density of a </span>liquid<span> you do the same thing you would for a solid. </span>
4 0
3 years ago
How to solve this question? please help me
Ber [7]

Use the Pythagorean theorem a^2 + b^2 = c^2

45^2 + 80^2 = c^2

2025 + 6400 = c^2

c^2 = 8425

c = √8425

c = 91.787

Rounded to the nearest foot = 92 feet

4 0
3 years ago
julio has 6 pounds of flour to make 5 cakes. if the cakes are equal in size how much flour will be used in each cake?​
NeTakaya

Answer:

6×5=30

Step-by-step explanation:

6 0
3 years ago
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