Question

An accounting professor is notorious for being stingy in giving out good letter grades. In a large section of 170 students in the fall semester, she gave out only 2% A's, 18% B's, 35% C's, and 45% D's and F's. Assuming that this was a representative class, compute the 85% confidence interval of the probability of getting at least a B from this professor. (You may find it useful to reference the z table. Round intermediate calculations to at least 4 decimal places. Round "z" value and final answers to 3 decimal places.)  

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = 0.18

Z_/2 = 1.44

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.44 * (((0.18 * 0.82) / 170)

= 0.042

A 85% confidence interval for population proportion p is ,

- E < p < + E

0.18 - 0.042 < p < 0.18 + 0.042

0.138 < p < 0.222

(0.138 , 0.222)