1. An Example of {AND, OR, Given that} Using a Normal Distribution By Henry Mesa

2. Consider the following problem. The length of human pregnancy in days, has an average of 266 days, and a standard deviation of 16 days. The distribution is normal. Let the random variable X denote the length of a human pregnancy.

3. Let event A be a pregnancy lasts between 266 days and 298 days. Let event B be a pregnancy lasts between 250 days 282 days. Let event C be a pregnancy lasts 234 days or less.

4. Consider the following problem. The length of human pregnancy in days, has an average of 266 days, and a standard deviation of 16 days. The distribution is normal. Let the random variable X denote the length of a human pregnancy. Let event A be a pregnancy lasts between 266 days and 298 days. Let event B be a pregnancy lasts between 250 days 282 days. Let event C be a pregnancy lasts 234 days or less. 1. Are events A and B disjoint? No, they share the common days 266 to 282.

5. Consider the following problem. The length of human pregnancy in days, has an average of 266 days, and a standard deviation of 16 days. The distribution is normal. Let the random variable X denote the length of a human pregnancy. Let event A be a pregnancy lasts between 266 days and 298 days. Let event B be a pregnancy lasts between 250 days 282 days. Let event C be a pregnancy lasts 234 days or less. 2. Are events B and C disjoint? Yes, they do not share any common days.

6. Consider the following problem. The length of human pregnancy in days, has an average of 266 days, and a standard deviation of 16 days. The distribution is normal. Let the random variable X denote the length of a human pregnancy. 3. Calculate P(B OR C) P(X < 234 OR 250 < X < 282) = = P(Z < -2) + P( -1< Z< 1 ) = 0.025 + 0.68 = 0.705 Using 68-95-99.7 rule Let event A be a pregnancy lasts between 266 days and 298 days. Let event B be a pregnancy lasts between 250 days 282 days. Let event C be a pregnancy lasts 234 days or less.

7. Consider the following problem. The length of human pregnancy in days, has an average of 266 days, and a standard deviation of 16 days. The distribution is normal. Let the random variable X denote the length of a human pregnancy. Let event A be a pregnancy lasts between 266 days and 298 days. Let event B be a pregnancy lasts between 250 days 282 days. Let event C be a pregnancy lasts 234 days or less. 3. Calculate P(B OR C) P(X < 234 OR 250 < X < 282) = = P(Z < -2) + P( -1< Z< 1 ) = 0.02275 + 0.68269 = 0.70544

8. Consider the following problem. The length of human pregnancy in days, has an average of 266 days, and a standard deviation of 16 days. The distribution is normal. Let the random variable X denote the length of a human pregnancy. Let event A be a pregnancy lasts between 266 days and 298 days. Let event B be a pregnancy lasts between 250 days 282 days. Let event C be a pregnancy lasts 234 days or less. 4. Calculate P(A OR B) P(250 < X < 282 OR 266 < X < 298) = = P( -1 < Z < 2 ) = 0.815 Using 68 –95-99.7 rule P(250 < X < 298) = 0.34 + 0.475