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madam [21]
3 years ago
6

If a normally distributed population has a mean (mu) that equals 100 with a standard deviation (sigma) of 18, what will be the c

omputed z-score with a sample mean (x-bar) of 106 from a sample size of 9?
Mathematics
1 answer:
garik1379 [7]3 years ago
7 0

Answer:

Z = 1

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 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.

Central Limit Theorem

The Central Limit Theorem establishes 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.

Mean (mu) that equals 100 with a standard deviation (sigma) of 18

\mu = 100, \sigma = 18

Sample of 9:

This means that n = 9, s = \frac{18}{\sqrt{9}} = 6

What will be the computed z-score with a sample mean (x-bar) of 106?

This is Z when X = 106. So

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

By the Central Limit Theorem

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

Z = \frac{106 - 100}{6}

Z = 1

So Z = 1 is the answer.

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If B is between A and C, and AB=3x+1 and BC=2x-7, and AC=19, then find the value of x.
kodGreya [7K]

Since AB and BC are two parts of AC, AC = AB + BC

let's plug the expressions from the question into our equation above.

19 = 3x + 1 + 2x - 7

Combine like terms

19 = 5x - 6

Add 6 to both sides.

25 = 5x

Divide both sides by 5

5 = x

8 0
3 years ago
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Describe the possible values for x and y when ∣x − y ∣ > 0. What does it mean when ∣x − y ∣ = 0? Can ∣x − y ∣ < 0? Explain
Vilka [71]
The possible values for | x-y | > 0 is any number above 0. x must be greater than y. When | x-y | = 0, That means that x and y are equal to each other. | x-y | can not be less than 0, but it can equal 0.

Hope that this helped!
4 0
3 years ago
Last Sunday, the average temperature was 8%, percent higher than the average temperature two Sundays ago. The average temperatur
MArishka [77]

Answer: 1.08T and (1+8/100)T


Step-by-step explanation:

Given: The average temperature two Sundays ago was T degrees Celsius.

Since, last Sunday, the average temperature was 8% higher than the average temperature two Sundays ago.

⇒ The average temperature last Sunday=8\%\ of\ T+T

Since 8%=0.08

Therefore, The average temperature last Sunday=\frac{8}{100}\timesT+T

⇒ The average temperature last Sunday=T(\frac{8}{100}+1)

⇒ The average temperature last Sunday=T(0.08+1)

⇒ The average temperature last Sunday=T(1.08)

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4 0
3 years ago
Please help with 6 and 7
Maru [420]

Answer:

6a) i- 2hrs 36mins  ii- 3hrs 12mins

b) car A≈ 76.9km/h  car B≈ 62.5km/h

c)------

7a) 35km

b) car A=75km  car B=60km

c) 30km

d) car A≈36mins  car B≈48mins

Step-by-step explanation:

6a) Using the graph follow the lines until they finish then go downwards until you get to the x-axis. The x-axis is going up by 12mins for each square.

b) Using the answer from a, you divide 200km by the time.

For car A 2hrs 36mins becomes 2.6 because 36mins/60mins=0.6

∴ car A: 200/2.6≈ 76.92km/h

For car B 3hrs 12mins becomes 3.2 because 12mins/60mins=0.2

∴ car B: 200/3.2≈ 62.5km/h

7a) Using the graph go down from where the line of car A finished to meet car B. The y-axis is going up by 5km for each square.

b) Starting from the x-axis at 1 hour go upwards to see where you meet the car B line (60km) and car A line(75km). (sorry if that does not really make sense).

c) Difference from car A line to car B:

155km-125km=30km

d) Going across from 50km meet car A line and go down to see it has been travelling for approx. 36mins. Then continue across to car B line, go down to see it reached 50km at approx. 48mins.

Hope this helps.

5 0
3 years ago
Can someone else me with the answer I think that it’s 93 degrees
inna [77]
Thank you for coming to Brainly with your questions!

I believe the answer is: 

93 degrees. You were correct. The interior angles all add up to 360, so you subtract each given angle to find the missing angle.

I hope this helps you! Please mark Brainliest! Let me know if I can help you with any further questions!

-Belle
7 0
3 years ago
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