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

By Henry Mesa

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**Consider the following problem**

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.

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**Consider the following problem**

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.

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**No, they share the common days 266 to 282.**

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.

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**Yes, they do not share any common days.**

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.

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**Consider the following problem**

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 ) = = Using rule

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**Consider the following problem**

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 ) = =

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**Consider the following problem**

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 ) = = 0.815Using 68 – rule

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**Consider the following problem**

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 ) = =

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**Consider the following problem**

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) = Using rule. =

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**Consider the following problem**

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) =

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**There is no chance that one observation can meet both criteria.**

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) = There is no chance that one observation can meet both criteria.

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**Consider the following problem**

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.

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**Consider the following problem**

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) = Given that the pregnancy lasted between 266 and 298 days, there is a % chance that this particular pregnancy lasted between 250 and 282 days.

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15.4 The Normal Distribution Objectives:

15.4 The Normal Distribution Objectives:

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