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An Example of {AND, OR, Given that} Using a Normal Distribution

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

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An Example of {AND, OR, Given that} Using a Normal Distribution

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  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. 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. 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. 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< 0 ) = 0.025 + 0.34 = 0.365 Using 68-95-99.7 rule

  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< 0 ) = 0.02275 + 0.34135 = 0.36410

  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(250 < X < 298) = P( -1 < Z < 2 ) = 0.34 + 0.475 = 0.815Using 68 –95-99.7 rule

  9. 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(P(250 < X < 282 OR 266 < X < 298) = P(250 < X < 298) = P( -1 < Z < 2 ) = 0.3414 +.4773 = 0.8187

  10. 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. 5. Calculate P(A AND B) P(250 < X < 282 AND 266 < X < 298) = P(266 < X < 282) = P(0 < Z < 1) = 0.34 Using 68-95-99.7 rule. = 0.34135

  11. 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. 5. Calculate P(A AND B) P(250 < X < 282 AND 266 < X < 298) = P(266 < X < 282) = P(0 < Z < 1) = 0.3413

  12. 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. 6. Calculate P(B AND C) P(X < 234 AND 250 < X < 282) = 0 There is no chance that one observation can meet both criteria.

  13. 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. The new whole/sample space. 7. Calculate P(A | B) = 0.5 Given that the pregnancy lasted between 250 and 282 days, there is a 50 % chance that this particular pregnancy lasted between 266 and 298 days.

  14. 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. The new whole/sample space. 8. Calculate P(B | A) = 0.7158 Given that the pregnancy lasted between 266 and 298 days, there is a 71.58 % chance that this particular pregnancy lasted between 250 and 282 days.

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