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Using the margin of error for the z-distribution, the sample sizes are given as follows:
a) 822.
b) 1068.
<h3>What is a confidence interval of proportions?</h3>A confidence interval of proportions is given by:
The margin of error is given by:
In which:
is the sample proportion.
- z is the critical value.
- n is the sample size.
We have a 95% confidence level, hence, z is the value of Z that has a p-value of
, so the critical value is z = 1.96.
Item a:
The estimate is of , hence we solve for n when M = 0.03.
n = 821.2
A sample of 822 is needed.
Item b:
No prior estimate, hence .
n = 1067.11
A sample of 1068 is needed.
More can be learned about the z-distribution at brainly.com/question/25890103
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Here, we are given with four fractions to multiply two of them and to add two of them. If we add them directly by taking the LCM and adding them is not a similar way. We can clearly observe that in those four fractions, we have two fractions as common i.e, we have two fractions as same. If we have two fractions or numbers as same, we can solve the sum by an other concept called as distributive property. In this property, we multiply the common fraction with the sum of other two fractions. This concept can also be done with fractions as well as integers. So, let's solve!!
Group the non-common fractions in bracket.
First we should solve the numbers in bracket.
LCM of 20 and 25 is 100.
Multiply the numerators and denominators in the bracket.
Now, write both numerators in bracket with a common denominator.
Now, add the numerators in bracket.
Write the numerator and denominator in lowest form by cancellation method.
Now, multiply the numerators and denominators.