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sergeinik [125]
2 years ago
7

Katie noticed that many of the students at her school ate fruit during lunch. She randomly chose 30 students and found that 18 o

f them ate fruit during lunch. If Katie sample is representative, which of the following is closest to the number of 1,560 students at her school who eat fruit at lunch?
Mathematics
1 answer:
LenKa [72]2 years ago
6 0

Answer:

52 / 1,560

Step-by-step explanation:

18 / 30

? / 1,560

1,560 / 30 = 52

52 / 1,560

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What is the value of x for 7x - 12 y = 180 / 7x = 84
katrin2010 [14]

eq^2: 7x=84 divide 84 by 7 which is 12.

therefore x is equal to 12. Then

1) take that 12 you got in equation 2 and substitute in equation 1 which is:

7x-12y=180

7(12)-12y=180

84 -12y=180

-12y=180-84

-12y=96 ............divide both sides with -12

-y=8 (×-1) both sides

y= -8

therefore 7(12)-12(-8)=180

5 0
3 years ago
According to 2013 report from Population Reference Bureau, the mean travel time to work of workers ages 16 and older who did not
gregori [183]

Answer:

a) 48.80% probability that his travel time to work is less than 30 minutes

b) The mean is 30.7 minutes and the standard deviation is of 3.83 minutes.

c) 13.13% probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes

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 = 30.7, \sigma = 23

a. If a worker is selected at random, what is the probability that his travel time to work is less than 30 minutes?

This is the pvlaue of Z when X = 30. So

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

Z = \frac{30 - 30.7}{23}

Z = -0.03

Z = -0.03 has a pvalue of 0.4880.

48.80% probability that his travel time to work is less than 30 minutes

b. Specify the mean and the standard deviation of the sampling distribution of the sample means, for samples of size 36.

n = 36

Applying the Central Limit Theorem, the mean is 30.7 minutes and the standard deviation is s = \frac{23}{\sqrt{36}} = 3.83

c. What is the probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes?

This is 1 subtracted by the pvalue of Z when X = 35. So

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

By the Central Limit Theorem

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

Z = \frac{35 - 30.7}{3.83}

Z = 1.12

Z = 1.12 has a pvalue of 0.8687

1 - 0.8687 = 0.1313

13.13% probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes

8 0
3 years ago
What is 15% off of 229.00 also a sales tax of 8%
gayaneshka [121]

Answer:

194.65

Step-by-step explanation:

3 0
3 years ago
36 + 12 = 3.
aleksley [76]

Answer:

12×3=36

Step-by-step explanation:

hope that helps you out

3 0
2 years ago
Solve for n.<br> d = 4m +7n
vitfil [10]

Step-by-step explanation:

d = 4m +7n

d - 4m = 7n

(d -4m)/7 = n

4 0
3 years ago
Read 2 more answers
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