Given that the relationship is linear.
The equation can be expressed as y = mx + c.
Substituting, when x = 0, we have y = 32.
Thus, 32 = c.......( 1 )
Then, when x = 100, y results in 212.
Which gives us:
212 = 100m + c.......( 2 )
By equating equations 1 and 2, we obtain:
100m = 212 - 32
Solving for x yields 1.8.
The final equation is therefore y = 1.8x + 32.
Hence, this represents the required solution.
Lacking information on the proportion, we will assume the sample proportion is 0.50
thus,
p = 0.50
The margin of error is set at 10 percentage points. This indicates that the error on either side of the population proportion is 5%, so E = 0.05
z = 1.645 (Z value for a confidence level of 90%)
The calculation for the margin of error when estimating population proportions follows:
Consequently, 271 students need to be part of the sample.