kimberlyvazquez1121
20.03.2020 •
Mathematics
The mean points obtained in an aptitude examination is 103 points with a variance of 169. What is the probability that the mean of the sample would differ from the population mean by less than 2.8 points if 63 exams are sampled? Round your answer to four decimal places.
Solved
Show answers
More tips
- C Computers and Internet How to Delete a Page on VKontakte: The Ultimate Guide from Experts...
- S Style and Beauty 5 Tips for Choosing the Best Ugg Boots...
- H Health and Medicine How to Treat the Flu: A Comprehensive Guide...
- H Health and Medicine Effective Ways to Treat Colic in Infants...
- C Computers and Internet IMHO: What is it, why is it important, and how to use it?...
- F Food and Cooking How to Calculate the Gender of Your Child with Blood?...
- S Style and Beauty How to Get Rid of Under Eye Bruises?...
- C Cities and Countries What time does the Metro open in Moscow?...
- W Work and Career Where can you learn to be a flight attendant?...
- H Health and Medicine What are Electronic Cigarettes? The Ultimate Guide...
Answers on questions: Mathematics
- M Mathematics What is the coefficient of the x2-term...
- M Mathematics Evaluate 16/6 - 2/9A 4 2/3B 2 2/3C 1 5/9D 2 4/9...
- M Mathematics A school district raises $7 a day by placing an ad on a school bus. If the ad runs 5 days a week for 39 weeks, how much money will the ad raise for the school district? A$1,365B$2,730C$1,540D$1,955...
- M Mathematics Four gallons of gasoline cost $14. A customer will get gallon for $3.50. A customer will get gallons for $7.00. A customer will get gallons for $14.00. A customer will pay $ for...
- M Mathematics What is the answer? -5x - 15 ≥ 20...
- M Mathematics You would draw a segmented bar graph A. to show the five-number-summary for the heights of female students. B.to detemne i gender and favorite toy as a child are associated. C.to...
- M Mathematics FREE POINTS FOR THE PEOPLEZ...
- M Mathematics which of the following equations describes the line passing through (3,-1) and parallel to the line described by y equals 2x + 0...
- M Mathematics Which equation represents a line which is parallel to x 0? ^^^^^...
- M Mathematics 17) Graph the following: a) [-3, 8) b) (−∞,−3] ∪ (8, ∞)...
Ответ:
0.9128 = 91.28% probability that the mean of the sample would differ from the population mean by less than 2.8 points if 63 exams are sampled
Step-by-step explanation:
To solve this question, we need 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 and standard deviation(which is the square root of the variance) , the zscore of a measure X is given by:
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 and standard deviation , the sample means with size n of at least 30 can be approximated to a normal distribution with mean and standard deviation
In this problem, we have that:
What is the probability that the mean of the sample would differ from the population mean by less than 2.8 points if 63 exams are sampled?
This is the pvalue of Z when X = 103+2.8 = 105.8 subtracted by the pvalue of Z when X = 103 - 2.8 = 100.2. So
X = 105.8
By the Central Limit Theorem
has a pvalue of 0.9564
X = 100.2
has a pvalue of 0.0436
0.9564 - 0.0436 = 0.9128
0.9128 = 91.28% probability that the mean of the sample would differ from the population mean by less than 2.8 points if 63 exams are sampled
Ответ: