Answer:
Step-by-step explanation:
A = 1/4 pie d2
= 1/4(22/7)(12)2
= 1/4(22/7)144
= 113.1
Using the normal distribution, the probabilities are given as follows:
a. 0.4602 = 46.02%.
b. 0.281 = 28.1%.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean
and standard deviation
is given by:

- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation
.
The parameters are given as follows:

Item a:
The probability is <u>one subtracted by the p-value of Z when X = 984</u>, hence:


Z = 0.1
Z = 0.1 has a p-value of 0.5398.
1 - 0.5398 = 0.4602.
Item b:

By the Central Limit Theorem:


Z = 0.58
Z = 0.58 has a p-value of 0.7190.
1 - 0.719 = 0.281.
More can be learned about the normal distribution at brainly.com/question/4079902
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Answer:
Step-by-step explanation:
You have to know how negative exponents "work" to understand this concept.
because if you want to make a negative exponent positive you put what the exponent is on under a 1. It follows then that you can go backwards from that and rewrite positive fractions with negative exponents.
You need to divide 179.10 by 6
Probaility in general is defined as the ratio of positive outcomes over the total number of outcomes.
In the first example, the total outcomes are 16; let us count the positive ones. There are 8 even numbers from 1-16. The prime numbers are 2,3,5,7,11,13. Out of those, only 5 are odd. Hence, in total there are 13 positive outcomes. Thus, the probability is 13/16=81.25%
Let's restrict the problem to the students that studied for the exam; the proportion is 0.57 of the total students. 0.52 of the total students studied and saw an increase in their exam. Hence, the probability that a student who studied saw an increse is 0.52/0.57 (here a positive outcome is the proportion that saw an increase and the total outcomes are all the students that studied). 0.52/0.57=91.22%