A military hero returned from Iraq and met his new-born child. After checking th

Question

A military hero returned from Iraq and met his new-born child. After checking the calendar and "doing the math" he was puzzled. He had been gone from June 1st, 2015 to April 15th, 2016 His wife claimed to have given birth 315 days after his last visit. The length of pregnancies are normally distributed with a mean of 266 days and a standard deviation of 18 days. Use the graph in Section 7. 1 to determine the approximate probabilities assigned to the Intervals the area between the points using mu = 266 and sigma = 18) on the graph SKETCH the graph of the normal distribution of the length of pregnancies. Determine the probability (without using the calculator) that the pregnancy is (#1) less than 266 days. (#2) more than 266 days Determine the probability (use the calculator) that the pregnancy is (#3) between 266 days and 315 days (#4) more than 315 days What is suggested by the probability that a pregnancy will last 315 days or longer? (#5)Interpret the probability. (minimum of 3 complete sentences) (#6) What is your advice to this military hero (minimum of3 complete sentences)

Explanation / Answer

1)P(X<266)=P(Z<(266-266)/18)=P(Z<0)=0.5

2)P(X>266)=0.5

3)P(266<X<315)=P(0<Z<(315-266)/18) =P(0<Z<2.7222)=0.9968-0.5=0.4968

4)P(X>315)=1-P(X<315)=1-0.9968=0.0032

5)above probabilty is giving birth for 315 or more days of pregnancy. from above it is calculated that there is 0.32% chance that pregnancy last that long. Hence it is considered to be an unusal event as probability of that

happening is less then 5%

6) as probabilty of that happening is very less. we can suspect an extramarital affair.for which he can go for DNA test of child. (:

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