Answer:
99% confidence interval for the population average examination score is between a lower limit of 69.2872 and an upper limit of 82.7128.
Step-by-step explanation:
Confidence interval = mean +/- margin of error (E)
mean = 76
variance = 144
sd = sqrt(variance) = sqrt(144) = 12
n = 25
degree of freedom (df) = n - 1 = 25 - 1 = 24
confidence level (C) = 99% = 0.99
significance level = 1 - C = 1 - 0.99 = 0.01 = 1%
t-value corresponding to 24 df and 1% significance level is 2.797
E = t×sd/√n = 2.797×12/√25 = 6.7128
Lower limit = mean - E = 76 - 6.7128 = 69.2872
Upper limit = mean + E = 76 + 6.7128 = 82.7128
99% confidence interval is (69.2872, 82.7128)
The total price before tax is $(38.75 +41.10) =79.85 and after tax the purchase price is 79.85 x 9.5% = $7.59 + $79.85= $87.44
Formula for the area of a circle: A = pi * r^2
A semi-circle is half of a circle. So, we will need to divide the area of the total circle by 2 to find the area of a semi-circle.
r = d / 2
r = 6 / 2 = 3
A = pi * 9
A = 9pi
Semi-circle:
A = 9pi / 2
A = 4.5 pi cm^2 or 14.14 cm^2
Hope this helps!! :)