1 / 14

Exploring Events in Normal Distribution of Human Pregnancy Lengths

This study analyzes the length of human pregnancies, modeled as a normal distribution with a mean of 266 days and a standard deviation of 16 days. We define three events: A (pregnancy lasts between 266 and 298 days), B (between 250 and 282 days), and C (234 days or less). We assess whether these events are disjoint and calculate their probabilities using the properties of normal distribution. Specific calculations for P(B OR C) and P(A AND B) are provided, demonstrating the application of the 68-95-99.7 rule in understanding event overlaps and probabilities in this biological context.

evers
Télécharger la présentation

Exploring Events in Normal Distribution of Human Pregnancy Lengths

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

More Related