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
By Henry Mesa
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.
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.
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.
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.
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) =234 266 250 266 282 266
P Z + P Z 16 16 16
= P(Z < -2) + P( -1< Z< 0 )
= 0.025 + 0.34
= 0.365 Using 68-95-99.7 rule
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) =234 266 250 266 282 266
P Z + P Z 16 16 16
= P(Z < -2) + P( -1< Z< 0 )
= 0.02275 + 0.34135
= 0.36410
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) =
250 266 298 266 = P Z
16 16
= P( -1 < Z < 2 )
= 0.815Using 68 –95-99.7 rule
P(250 < X < 298)
= 0.34 + 0.475
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) =
250 266 298 266 = P Z
16 16
= P( -1 < Z < 2 )
= 0.3414 +.4773
= 0.8187
P(250 < X < 298)
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) =
266 266 282 266 = P Z
16 16
= P(0 < Z < 1)
= 0.34 Using 68-95-99.7 rule.
= 0.34135
P(266 < X < 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.
5. Calculate P(A AND B)
P(250 < X < 282 AND 266 < X < 298) =
266 266 282 266 = P Z
16 16
= P(0 < Z < 1)
= 0.3413
P(266 < X < 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.
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.
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.
7. Calculate P(A | B)
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.
P(A AND B) =
P(B)
P(266 < X < 282) =
P(250<X<282)
The new whole/sample space.
0.34 =
0.68
= 0.5
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.
8. Calculate P(B | A)
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.
P(A AND B) =
P(A)
P(266 < X < 282) =
P(266 < X < 298)
The new whole/sample space.
0.34 =
0.475
= 0.7158