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Olin [163]
3 years ago
10

Which of the following values would complete the ordered pair if the point is on the graph of f (x) = -3x + 2 ?

Mathematics
1 answer:
guajiro [1.7K]3 years ago
8 0
Two negatives create a positive number. -3 ×-1=3 So, 3+2=5
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The overhead reach distances of adult females are normally distributed with a mean of 197.5 cm197.5 cm and a standard deviation
fiasKO [112]

Answer:

a) 5.37% probability that an individual distance is greater than 210.9 cm

b) 75.80% probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

c) Because the underlying distribution is normal. We only have to verify the sample size if the underlying population is not normal.

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 question, we have that:

\mu = 197.5, \sigma = 8.3

a. Find the probability that an individual distance is greater than 210.9 cm

This is 1 subtracted by the pvalue of Z when X = 210.9. So

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

Z = \frac{210.9 - 197.5}{8.3}

Z = 1.61

Z = 1.61 has a pvalue of 0.9463.

1 - 0.9463 = 0.0537

5.37% probability that an individual distance is greater than 210.9 cm.

b. Find the probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

Now n = 15, s = \frac{8.3}{\sqrt{15}} = 2.14

This probability is 1 subtracted by the pvalue of Z when X = 196. Then

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

By the Central Limit Theorem

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

Z = \frac{196 - 197.5}{2.14}

Z = -0.7

Z = -0.7 has a pvalue of 0.2420.

1 - 0.2420 = 0.7580

75.80% probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

The underlying distribution(overhead reach distances of adult females) is normal, which means that the sample size requirement(being at least 30) does not apply.

5 0
3 years ago
Plss can someone help me out with thissss!!!!!!!!!!!
KengaRu [80]
If there aren’t any degrees and it doesn’t state that the triangle is equilateral then you cannot solve this equation without more information
4 0
2 years ago
The sum of three consecutive numbers is equal to 123. What are the numbers?
Zina [86]

Answer:

40, 41, 42

Step-by-step explanation:

x +x+1+x+2=123

3x+3=123

3x=123-3

3x=120

x=120:3

x=40(the first number

40+1=41 (the second number

40+2=42 (the third number

4 0
3 years ago
Augustin has 20 different chess boards. If he played 3 games per day, each game played on a different board, how long would it t
Nutka1998 [239]

Answer:

514 days

Step-by-step explanation:

We use the formula (r+n-1)/r(n-1)

There are 1540 combinations. Then, we'll divide them by three because were not just finding the amount of combinations, but the time it'd take to play them all.

We get 513.333(cont.)

thats not really possible, so we're gonna go with 514 instead, rounding up. Normally we'd round down, because the number behind the decimal is below 5, but we really want to make sure we get every combination in there.

Hope this is helpful!

8 0
3 years ago
The sum of 6 consecutive integers is 519
Zielflug [23.3K]

i don't understand, what is it asking for here?

3 0
2 years ago
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