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ipn [44]
3 years ago
12

How do I do this problem??

Mathematics
1 answer:
Montano1993 [528]3 years ago
8 0
The answer to this problem is 1 :)
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The mean points obtained in an aptitude examination is 159 points with a standard deviation of 13 points. What is the probabilit
Korolek [52]

Answer:

0.4514 = 45.14% probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled

Step-by-step explanation:

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

Normal probability distribution:

Problems of normally distributed samples are solved using 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 random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 159, \sigma = 13, n = 60, s = \frac{13}{\sqrt{60}} = 1.68

What is the probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled?

This is the pvalue of Z when X = 159+1 = 160 subtracted by the pvalue of Z when X = 159-1 = 158. So

X = 160

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

By the Central Limit Theorem

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

Z = \frac{160 - 159}{1.68}

Z = 0.6

Z = 0.6 has a pvalue of 0.7257

X = 150

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

Z = \frac{158 - 159}{1.68}

Z = -0.6

Z = -0.6 has a pvalue of 0.2743

0.7257 - 0.2743 = 0.4514

0.4514 = 45.14% probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled

7 0
3 years ago
In sporting tournaments, teams are eliminated after they lose. The number of teams in the
tresset_1 [31]

38 teams started.

16×3=38

7 0
2 years ago
Given the following winning percentages of the teams in a league (for a single year) compute the within-season standard deviatio
Masja [62]

Answer:

(b) 0.251

Step-by-step explanation:

1. Standard deviation equation:

SD=\sqrt{\frac{\sum\limits^N_i {(x_{i}-X)^{2}  } }{N} }

Where X is the mean of the data, and N the amount of data. Then, N=5

2. Estimate the Mean:

X=\frac{0.750+0.750+0.200+0.600+0.200}{5}=\frac{2.5}{5}=0.5\\

3. Caclulate Standard deviation:

SD=\sqrt{\frac{{(0.750-0.500)^{2}+(0.750-0.500)^{2}+(0.200-0.500)^{2}+(0.600-0.500)^{2}+(0.200-0.500)^{2}  } }{5} }

SD=\sqrt{\frac{0.315}{5} }=\sqrt{0.063}\\SD=0.251

7 0
2 years ago
Please answer this for me SHOW WORK 60 points and brainliest
Sliva [168]

Answer:

OMG YES THANKS IF U EVER COMMENT ON MY QUESTION I WILL KEEP PUTTING RANDOME STUFF MWAH

Step-by-step explanation:

3 0
3 years ago
The length of side AI is?
marissa [1.9K]

Answer:

AI=3.25 IH= 4.2

Step-by-step explanation

The distance between C and D is 1.3 inches, the distance between E and F is 0.75 inches and the distance between G and H is 1.2 inches. This is true because the model says so. If you look closely together, this is equal to the distance between AI which is the length of AI. The answer would be 1.2+1.3+0.75=3.25. To find the length of side IH you do the same strategy, the distance between sides D and E is 4.8 inches, at the bottom is 9 inches of distance between side I and side F. 9-4.8 inches is equal to 4.2 inches. Therefore, the length of side AI is 3.25 inches and the length of side IH is 4.2 inches. If I am wrong please tell me for feedback, I also hoped that this has helped you in your learning :)

3 0
2 years ago
Read 2 more answers
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