Can i get some help

The mean number of words per minute (WPM) read by sixth graders is 8888 with a standard deviation of 1414 WPM. If 137137 sixth g

Bingel [31]

Noticing that there is a pattern of repetition in the question (the numbers are repeated twice), we are assuming that the mean number of words per minute is 88, the standard deviation is of 14 WPM, as well as the number of sixth graders is 137, and that there is a need to estimate the probability that the sample mean would be greater than 89.87.

Answer:

"The probability that the sample mean would be greater than 89.87 WPM" is about $\\ P(z>1.56) = 0.0594$ .

Step-by-step explanation:

This is a problem of the distribution of sample means. Roughly speaking, we have the probability distribution of samples obtained from the same population. Each sample mean is an estimation of the population mean, and we know that this distribution behaves normally for samples sizes equal or greater than 30 $\\ n \geq 30$ . Mathematically

$\\ \overline{X} \sim N(\mu, \frac{\sigma}{\sqrt{n}})$ [1]

In words, the latter distribution has a mean that equals the population mean, and a standard deviation that also equals the population standard deviation divided by the square root of the sample size.

Moreover, we know that the variable Z follows a normal standard distribution, i.e., a normal distribution that has a population mean $\\ \mu = 0$ and a population standard deviation $\\ \sigma = 1$ .

$\\ Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}$ [2]

From the question, we know that

The population mean is $\\ \mu = 88$ WPM
The population standard deviation is $\\ \sigma = 14$ WPM

We also know the size of the sample for this case: $\\ n = 137$ sixth graders.

We need to estimate the probability that a sample mean being greater than $\\ \overline{X} = 89.87$ WPM in the distribution of sample means. We can use the formula [2] to find this question.

The probability that the sample mean would be greater than 89.87 WPM

$\\ Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$\\ Z = \frac{89.87 - 88}{\frac{14}{\sqrt{137}}}$

$\\ Z = \frac{1.87}{\frac{14}{\sqrt{137}}}$

$\\ Z = 1.5634 \approx 1.56$

This is a standardized value and it tells us that the sample with mean 89.87 is 1.56 standard deviations above the mean of the sampling distribution.

We can consult the probability of P(z<1.56) in any cumulative standard normal table available in Statistics books or on the Internet. Of course, this probability is the same that $\\ P(\overline{X} < 89.87)$ . Then

$\\ P(z$

However, we are looking for P(z>1.56), which is the complement probability of the previous probability. Therefore

$\\ P(z>1.56) = 1 - P(z$

$\\ P(z>1.56) = P(\overline{X}>89.87) = 0.0594$

Thus, "The probability that the sample mean would be greater than 89.87 WPM" is about $\\ P(z>1.56) = 0.0594$ .

5 0

3 years ago

941 rounded to the nearest 10

Oksana_A [137]

Answer:

900

Step-by-step explanation:

you just see if by the number, if the number is 6 and up your round over and it would become 950 but the number is lower so you make it 900.

3 0

2 years ago

What is the common difference of the sequence 8, 4, 0, -4, -16?

soldier1979 [14.2K]

$\large \mathfrak{Solution : }$

Common difference of an Arithmetic progression can be found out by subtracting the preceding term from that given term.

i.e

$common \: \: difference = 4 - 8$
$common \: \: difference = - 4$

therefore, the common difference of the above Arithmetic progression is -4 .

7 0

2 years ago

What is the simplified form of (–3x3y2)(5xy–1)?

ololo11 [35]

The answer is -15x3y2***

5 0

3 years ago

A rectangular prism with a volume of 44 cubic units is filled with cubes with side lengths of 1/3 unit How many 1/3 unit cubes d

pickupchik [31]

Check the picture below.

so the volume of the smaller cube will just be (1/3)³.

how many of those cubes will take to fill up the larger cube?

namely

how many times does (1/3)³ go into 44?

$\bf \left( \cfrac{1}{3} \right)^3\implies \cfrac{1^3}{3^3}\implies \cfrac{1}{27}\impliedby \textit{volume of the smaller cube} \\\\\\ 44\div \cfrac{1}{27}\implies \cfrac{44}{1}\div \cfrac{1}{27}\implies \cfrac{44}{1}\cdot \cfrac{27}{1}\implies 1188$

7 0

3 years ago

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