If a rectangle has a width of 5 meters and a perimeter of 50 meters calculate the area.
2 answers:
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Using the <em>normal distribution and the central limit theorem</em>, we have that:
a) A normal model with mean 0.3 and standard deviation of 0.0458 should be used.
b) There is a 0.2327 = 23.27% probability that more than one third of this sample wear contacts.
<h3>Normal Probability Distribution</h3>In a normal distribution with mean and standard deviation
, the z-score of a measure X is given by:
- It 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, which is the percentile of X.
- By the Central Limit Theorem, for a <u>proportion p in a sample of size n</u>, the sampling distribution of sample proportion is approximately normal with mean
and standard deviation
, as long as
and
.
In this problem:
- 30% of students at a university wear contact lenses, hence p = 0.3.
- We randomly pick 100 students, hence n = 100.
Item a:
Hence a normal model is appropriated.
The mean and the standard deviation are given as follows:
Item b:
The probability is <u>1 subtracted by the p-value of Z when X = 1/3 = 0.3333</u>, hence:
By the Central Limit Theorem
has a p-value of 0.7673.
1 - 0.7673 = 0.2327.
0.2327 = 23.27% probability that more than one third of this sample wear contacts.
To learn more about the <em>normal distribution and the central limit theorem</em>, you can take a look at brainly.com/question/24663213
Since
where the sign depends on the location of the terminal side of the angle. Since the terminal side lies in the fourth quadrant, that means the cosine of the angle is positive, so