Perform a continuity correction to rewrite the probability P (100? x < 115) that involves a discrete random variable (x) as a probability involving a continuous random variable (x'). a. P (100.5 < x' < 115.5) b. P (99.5 < x' < 115.5) c. P (100.5 < x' < 114.5)

d. P (99.5 < x' < 114.5)

Option B

Step-by-step explanation:

Given:

- P (100 < = x' < = 115)

Find:

- The correct expression for continuity correction:

Solution:

- For continuity correction we will observe the signs for each limit '' ", " ".

- The given expressions has the sign " ". For continuity correction i. e required for binomial distribution approximation with normal distribution. Since normal distribution can not compute probability " = " or any equals to sign. We convert the " = " sign to equivalent " " signs.

- So, to convert " 100 < = x' " into " a 99.

Then we find and average between the two i. e 99.5. So correction for LHS of expression is (99.5 < = x').

- Similarly for RHS we have " x' < = 115 " we need to convert it into " x' < a ".

We can write it as x'< 116. Now again take average of the two numbers Left and right we have 115.5. Hence, (x' < 155.5)

- The final expression is: P (99.5 < x' < 155.5) @ which normal approximation is to be performed. Option B