Will someone please, please help me solve these problems please. I desperately need your help Thanks?

2. ANSWER: 95% Level of Confidence SAMPLE SIZE = 2401

Why???

CHOOSING THE SAMPLE SIZE, POPULATION PROPORTION

π: POPULATION PROPORTION = 50

(50% - assumption)

B: SPECIFIED BOUND ON THE ERROR = 0.02

significant digits = 2

Level of Confidence = 95

'z critical value' from Look-up Table for 95% = 1.96

FORMULA FOR COMPUTATION OF SAMPLE SIZE:

B = 'z critical value' * SQRT [ π * (1 - π )/n]

Algebraically solve for SAMPLE SIZE n :

n = π * (1 - π) * [ 'z critical value' / B ]² = 0.5 * (1 - 0.5) * [ 1.96 / 0.02 ]²

SAMPLE SIZE = 2401

The Table for Standard Normal Distribution is organized as a cummulative 'area' from the LEFT corresponding to a 'z critical value'. The Standard Normal Distribution is also symmetric (called a 'Bell Curve') which means its an interpretive procedure to Look-Up the 'area' from the Table. For Level of Confidence = 95 the Look-Up 'z critical value' = -1.96 which corresponds to the 'area' from the LEFT outside of the Level of Confidence.

And since the Table for Standard Normal Distribution is symmetric, the 'area' from the LEFT is one-half outside of the Level of Confidence. There is also another one-half from the RIGHT as well. For the purpose of solving this question, the Look-Up 'z critical value' from the LEFT is satisfactory.

Alternatively; use Excel NORMSINV(probability) = NORMSINV ( 0.5*( 1 - 95 / 100 )))

3. ANSWER: Sample Size = 97 for 95% level of confidence

Why???

SMALL SAMPLE, LEVEL OF CONFIDENCE, NORMAL POPULATION DISTRIBUTION

Margin of Error (half of confidence interval) = 1

The margin of error is defined as the "radius" (or half the width) of a confidence interval for a particular statistic.

Level of Confidence = 95

σ: population standard deviation = 5

('z critical value') from Look-up Table for 95% = 1.96

The Look-up in the Table for the Standard Normal Distribution utilizes the Table's cummulative 'area' feature. The Table shows positve and negative values of ('z critical') but since the Standard Normal Distribution is symmetric, only the magnitude of ('z critical') is important.

For a Level of Confidence = 95% the corresponding LEFT 'area' = 0.48. And due to Table's symmetric nature, the corresponding RIGHT 'area' = 0.48 The ('z critical') value Look-up is 1.96

significant digits = 2

Margin of Error = ('z critical value') * σ/SQRT(n)

n = Sample Size

Algebraic solution for n:

n = [('z critical value') * σ/Margin of Error]²

= [ (1.96 * 5)/1 ]²

Sample Size = 97 for 95% level of confidence