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ziro4ka [17]
3 years ago
10

"How much do students pay, on average, for textbooks during the first semester in college? From a random sample of 400 students

the mean cost was found to be $357.75 ,and the sample standard deviation was $37.89. Assuming that the population is normally distributed, find the margin of error of a 95% confidence interval for the population mean. Compute the confidence interval and describe in words what it means."
Mathematics
1 answer:
dezoksy [38]3 years ago
7 0

Answer: The margin of error = 3.71, confidence interval = (354.04, 361.46) and it means that mean cost is lies within the confidence interval.

Step-by-step explanation:

Since we have given that

Sample size = 400

Mean = $357.75

Standard deviation = $37.89

At 95% confidence level, z = 1.96

We first find the margin of error.

Margin of error is given by

z\times \dfrac{\sigma}{\sqrt{n}}\\\\=1.96\times \dfrac{37.89}{\sqrt{400}}\\\\=3.71

95% confidence interval would be

\bar{x}\pm \text{margin of error}\\\\=357.75\pm 3.71\\\\=(357.75-3.71,357.75+3.71)\\\\=(354.04,361.46)

Hence, the margin of error = 3.71, confidence interval = (354.04, 361.46) and it means that mean cost is lies within the confidence interval.

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The graph is continuous.A viable solution is (10, 50) at the function t = c + 40.

The complete question is given below:-

The temperature, t, in degrees Fahrenheit, can be found by counting the number of cricket chirps, c, heard in 14 seconds and then adding 40. The equation t = c + 40 models the relationship between the temperature and the number of cricket chirps. What is true about the graph that represents this real-world scenario? Check all that apply.

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A viable solution is (10, 50).

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The given equation is

t = c + 40

This equation models the relationship between the temperature and the number of cricket chirps.

Where is the temperature in degrees Fahrenheit and is the number of cricket chirps heard in 14 seconds?

According to the problem, the temperature can be found by counting the number of cricket chirps heard in 14 seconds and then adding 40.

Now, the choices to this question are

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A viable solution is (0.5, 40.5).

A viable solution is (10, 50).

The graph of the given equation is attached, it shows the linear relationship between both variables.

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