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3 years ago

5. TEMPERATURES The table shows the low temperatures in degrees Fahrenheit for the past week

Mathematics

1 answer:

lorasvet [3.4K]3 years ago

6 0

Daniela made her error on step 3 because it says:

"Find the ratio of the differences of the means compared to the mean absolute deviation.

She didn't find the difference between the today and last week means. She just put the mean as a whole.

You might be interested in

The probability of winning a prize at a school raffle is 0.62. What is the probability of not winning a prize

mixas84 [53]

Answer:

b. 0.38.

Step-by-step explanation:

You either win a prize or you don't. There are only 2 possibilities so the probability of not winning a prize = 1 - 0.62 = 0.38.

7 0

3 years ago

Q # 15 I need help please to resolve

kow [346]

The sequence is

740, 707.60,675.20,642.80,...

Here first term is 740, and common difference, d is

$707.60-740 = -32.40$

Now we use the formula of nth term, which is

$a_{n} = a+(n-1)d$

Substituting the values of a,n and d, we will get

$=740+(n-1)(-32.40), 23 months$

Correct option is the second option .

7 0

3 years ago

The average amount of water in randomly selected 16-ounce bottles of water is 16.15 ounces with a standard deviation of 0.45 oun

vekshin1

Answer:

0.0179 = 1.79% probability that the mean of this sample is less than 15.99 ounces of water.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use 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:

$\mu = 16.15, \sigma = 0.45, n = 35, s = \frac{0.45}{\sqrt{35}} = 0.0761$

What is the probability that the mean of this sample is less than 15.99 ounces of water?

This is the pvalue of Z when X = 15.99. So

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

By the Central Limit Theorem

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

$Z = \frac{15.99 - 16.15}{0.0761}$

$Z = -2.1$

$Z = -2.1$ has a pvalue of 0.0179

0.0179 = 1.79% probability that the mean of this sample is less than 15.99 ounces of water.

3 0

3 years ago

A square banquet hall has a 3600m2 area. What is the length of the room?

Assoli18 [71]

The answer should be 10.

8 0

3 years ago

Read 2 more answers

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Anettt [7]

Answer:

Choice C: approximately 121 green beans will be 13 centimeters or shorter.

Step-by-step explanation:

What's the probability that a green bean from this sale is shorter than 13 centimeters?

Let the length of a green bean be $X$ centimeters.

$X$ follows a normal distribution with

mean $\mu = 11.2$ and
standard deviation $\sigma = 2.1$ .

In other words,

$X\sim \text{N}(11.2, 2.1^{2})$ ,

and the probability in question is $X \le 13$ .

Z-score table approach:

Find the z-score of this measurement:

$\displaystyle z= \frac{x-\mu}{\sigma} = \frac{13-11.2}{2.1} = 0.857143$ . Closest to 0.86.

Look up the z-score in a table. Keep in mind that entries on a typical z-score table gives the probability of the left tail, which is the chance that $Z$ will be less than or equal to the z-score in question. (In case the question is asking for the probability that $Z$ is greater than the z-score, subtract the value from table from 1.)

$P(X\le 13) = P(Z \le 0.857143) \approx 0.8051$ .

"Technology" Approach

Depending on the manufacturer, the steps generally include:

Locate the cumulative probability function (cdf) for normal distributions.
Enter the lower and upper bound. The lower bound shall be a very negative number such as $-10^{9}$ . For the upper bound, enter $13$
Enter the mean and standard deviation (or variance if required).
Evaluate.

For example, on a Texas Instruments TI-84, evaluating $\text{normalcdf})(-1\text{E}99,\;13,\;11.2,\;2.1 )$ gives $0.804317$ .

As a result,

$P(X\le 13) = 0.804317$ .

Number of green beans that are shorter than 13 centimeters:

Assume that the length of green beans for sale are independent of each other. The probability that each green bean is shorter than 13 centimeters is constant. As a result, the number of green beans out of 150 that are shorter than 13 centimeters follow a binomial distribution.

Number of trials $n$ : 150.
Probability of success $p$ : 0.804317.

Let $Y$ be the number of green beans out of this 150 that are shorter than 13 centimeters. $Y\sim\text{B}(150,0.804317)$ .

The expected value of a binomial random variable is the product of the number of trials and the probability of success on each trial. In other words,

$E(Y) = n\cdot p = 150 \times 0.804317 = 120.648\approx 121$

The expected number of green beans out of this 150 that are shorter than 13 centimeters will thus be approximately 121.

7 0

3 years ago