Using the <em>normal probability distribution and the central limit theorem</em>, it is found that the probabilities are given by:
a) 0.0119 = 1.19%.
b) 0.121 = 12.1%.
c) 0.9257 = 92.57%.
<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, the sampling distribution of sample means of size n has standard deviation .
In this problem:
- The mean is of .
- The standard deviation is of .
- A sample of 144 is taken, hence .
Item a:
The probability is the <u>p-value of Z when X = 42600</u>, hence:
By the Central Limit Theorem:
has a p-value of 0.0119.
The probability is of 0.0119 = 1.19%.
Item b:
The probability is the <u>1 subtracted by the p-value of Z when X = 46240</u>, hence:
has a p-value of 0.879.
1 - 0.879 = 0.121.
The probability is of 0.121 = 12.1%.
Item c:
The probability is the <u>p-value of Z when X = 46980 subtracted by the p-value of Z when X = 43190</u>, hence:
X = 46980:
has a p-value of 0.9693.
X = 43190:
has a p-value of 0.0436.
0.9693 - 0.0436 = 0.9257.
The probability is of 0.9257 = 92.57%.
To learn more about the <em>normal probability distribution and the central limit theorem</em>, you can check brainly.com/question/24663213
Answer:
1
Step-by-step explanation:
8x^2-5x-2
method
open bracket
6x^2-2x-3+x^2-3x+1
collect like terms
6x^2+2x^2-3-3x+1
8x^2-3-3x+1
again collect like terms
8x^2-2x-3x-3+1
8x^2-5x-3+1. (-×-=+ addition but keeping sign minus
8x-5x-2. (-×+=-)
Answer:
D: 113.04
Step-by-step explanation:
Volume cone formula: V=πr^2h/3
V = π(6)^2 3/3
V = 113.1
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