How are real numbers used to describe real-world situations?

1 answer:

7 0

Real numbers are all the rational numbers such as -7 and 4/3 and all irrational numbers. Real numbers are used mainly in counting and are used in measurement which is always present in real-world situations. These numbers help us to quantify things around.

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Past experience has indicated that the breaking strength of yarn used in manufacturing drapery material is normally distributed

vlabodo [156]

Answer:

95% two-sided confidence interval on the true mean breaking strength is (94.8cm, 99.2cm)

Step-by-step explanation:

Our sample size is 11.

The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So

$df = 11-1 = 10$ .

Then, we need to subtract one by the confidence level $\alpha$ and divide by 2. So:

$\frac{1-0.95}{2} = \frac{0.05}{2} = 0.025$

Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 10 and 0.025 in the two-sided t-distribution table, we have $T = 1.812$

Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So

$s = \frac{4}{\sqrt{11}} = 1.2060$

Now, we multiply T and s

$M = Ts = 1.812*1.2060 = 2.19/tex]For the lower end of the interval, we subtract the sample mean by M. So the lower end of the interval here is[tex]L = 97 - 2.19 = 94.81 = 94.8$ cm

For the upper end of the interval, we add the sample mean and M. So the upper end of the interval here is

$L = 97 + 2.19 = 99.19 = 99.2$ cm

95% two-sided confidence interval on the true mean breaking strength is (94.8cm, 99.2cm).

7 0

3 years ago

What is the probability of getting a sum 9 from two throws of a dice?

Fittoniya [83]

1/9 is the answer for that question

8 0

3 years ago

Read 2 more answers

A college-entrance exam is designed so that scores are normally distributed with a mean of 500 and a standard deviation of 100.

Crank

Answer: 1.25

Step-by-step explanation:

Given: A college-entrance exam is designed so that scores are normally distributed with a mean $(\mu)$ = 500 and a standard deviation $(\sigma)$ = 100.