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Stells [14]
3 years ago
8

I need help again lol

Mathematics
1 answer:
Alex787 [66]3 years ago
7 0

Answer:9

Step-by-step explanation:

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The composite scores of individual students on the ACT college entrance examination in 2009 followed a normal distribution with
Mumz [18]

Answer:

35.57% probability that a single student randomly chosen from all those taking the test scores 23 or higher.

0.41% probability that a simple random sample of 50 students chosen from all those taking the test has an average score of 23 or higher.

The lower the standard deviation, the higher the z-score, which means that the higher the pvalue of X = 23, which means there is a lower probability of scoring above 23. By the Central Limit Theorem, as the sample size increases, the standard deviation decreases, which means that Z increases.

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 = 21.1, \sigma = 5.1

What is the probability that a single student randomly chosen from all those taking the test scores 23 or higher?

This is the pvalue of Z when X = 23.

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

Z = \frac{23 - 21.1}{5.1}

Z = 0.37

Z = 0.37 has a pvalue of 0.6443

1 - 0.6443 = 0.3557

35.57% probability that a single student randomly chosen from all those taking the test scores 23 or higher.

What is the probability that a simple random sample of 50 students chosen from all those taking the test has an average score of 23 or higher?

Now we use the central limit theorem, so n = 50, s = \frac{5.1}{\sqrt{50}} = 0.72

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

Z = \frac{23 - 21.1}{0.72}

Z = 2.64

Z = 2.64 has a pvalue of 0.9959

1 - 0.9959 = 0.0041

0.41% probability that a simple random sample of 50 students chosen from all those taking the test has an average score of 23 or higher.

Why is it more likely that a single student would score this high instead of the sample of students?

The lower the standard deviation, the higher the z-score, which means that the higher the pvalue of X = 23, which means there is a lower probability of scoring above 23. By the Central Limit Theorem, as the sample size increases, the standard deviation decreases, which means that Z increases.

5 0
3 years ago
Use the parabola tool to graph the quadratic function. f(x)=2x2+12x+16
yKpoI14uk [10]
We have that
<span>f(x)=2x</span>²<span>+12x+16

using a graph tool
see the attached figure</span>

7 0
3 years ago
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Please help I’ll give 30 poins
Jobisdone [24]
Part a= cuboid

Part b= To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.*I tried my best sorry*
3 0
2 years ago
Read 2 more answers
Find the measurement
xenn [34]

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

6z + 7  = 8z - 9

8z - 9 = 6z + 7

Add sides 9

8z - 9 + 9 = 6z + 7 + 9

8z = 6z + 16

Subtract sides 6z

- 6z + 8z =  - 6z + 6z + 16

2z = 16

Divide sides by 2

\frac{2z}{2}  =  \frac{16}{2}  \\

z = 8

Thus ;

NP = 8z - 9

NP = 8(8) - 9

NP = 64 - 9

NP = 64 - 4 - 5

NP = 60 - 5

NP = 55

Done...

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

6 0
3 years ago
2 Look at the open number line in<br> Problem 1. How would you change the<br> numbers to show 9 + 5?
-BARSIC- [3]

Answer:

i need the number line

Step-by-step explanation:

lol

8 0
3 years ago
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