Question

Consider the probability that no more than 28 out of 304 students will not graduate on time. Choose the best description of the area under the normal curve that would be used to approximate binomial probability.

a. Area to the right of 27.5
b. Area to the right of 28.5
c. Area to the left of 27.5
d. Area to the left of 28.5
e. Area between 27.5 and 28.5

Answer 1

Here the probability that exactly 28 out of 304 students will not graduate on time. That is

P (x = 28)

By using the normal approximation of binomial probability,

`$P(x=a) = P(a-1/2 \leq x \leq a+1/2)$`

∴
`$P(x=28) = P(28-1/2 \leq x \leq 28+1/2)$`

`$=P(27.5 \leq x \leq 28.5)$`

That is the area between 27.5 and 28.5

Therefore, the correct option is (e). Area between 27.5 and 28.5