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
The answer to the question
You are basically asking 160% of X = 70.
1) 70 x 100 = 7000 (to turn the 70 into a %)
2) 7000 /160 = 43.75
You can reverse the equation to double check the answer.
160% x 43.75 = 70
Answer:
1306.24 cm².
Step-by-step explanation:
From the diagram given above, we obtained the following information:
Radius (r) = 13 cm
Pi (π) = 3.14
Slant height (l) = 19 cm
Surface Area (SA) =.?
The surface area of the cone can be obtained as follow:
SA = πr² + πrl
SA = πr ( r + l)
SA = 3.14 × 13 ( 13 + 19)
SA = 40.82 (32)
SA= 1306.24 cm²
Therefore, the surface area of the cone is 1306.24 cm².