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evablogger [386]
3 years ago
6

Im having trouble on this

Mathematics
1 answer:
Degger [83]3 years ago
3 0

Answer: girl no

Step-by-step explanation:

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A researcher reports survey results by stating that the standard error of the mean is 25 the population standard deviation is 40
bezimeni [28]

Answer:

a) A sample of 256 was used in this survey.

b) 45.14% probability that the point estimate was within ±15 of the population mean

Step-by-step explanation:

This question is solved using 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.

a. How large was the sample used in this survey?

We have that s = 25, \sigma = 400. We want to find n, so:

s = \frac{\sigma}{\sqrt{n}}

25 = \frac{400}{\sqrt{n}}

25\sqrt{n} = 400

\sqrt{n} = \frac{400}{25}

\sqrt{n} = 16

(\sqrt{n})^2 = 16^2[tex][tex]n = 256

A sample of 256 was used in this survey.

b. What is the probability that the point estimate was within ±15 of the population mean?

15 is the bounds with want, 25 is the standard error. So

Z = 15/25 = 0.6 has a pvalue of 0.7257

Z = -15/25 = -0.6 has a pvalue of 0.2743

0.7257 - 0.2743 = 0.4514

45.14% probability that the point estimate was within ±15 of the population mean

3 0
3 years ago
Yall are doing great thanks sm for the help
blondinia [14]

Answer:

That is an obtuse isosceles

4 0
3 years ago
This morning, Maria's car had 16.03 gallons of fuel. Now, 2.9 gallons are left. How much fuel did Maria use?
Vadim26 [7]

Answer:

take 16.03 and subtract 2.9

16.03-2.9=13.13

so maria used 13.13 gallons

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
What is 5p+2q-3p-3q
aivan3 [116]
2p-1q is the answer 
5p+2q-3p-3q
isolate the variables:
5p-3p+2q-3q
simplify:
2p-1q
that is the answer! 
hope I helped! :)
8 0
3 years ago
Read 2 more answers
The profit a company earns every month depends on the amount of product sold,p, for $855 each and the amount spent in rent, util
Rina8888 [55]

the CEO earns about <em><u>31045.5</u></em> in a given month

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3 years ago
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