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

Question

A military hero returned from Iraq and met his new - boom child. After checking the calendar and "doing the math", he was puzzled. He had been gone from June 1^st, 2015 to April 15^th, 2016. His wife claimed to have given birth 315 days after his last visit. The length of pregnancies is 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. 50% more than 266 days. Determine the probability (use the calculator) that the pregnancy is (#3) between 266 days and 315 days. more than 315 days. What is suggested by the probability that a pregnancy will last 315 days or longer? Interpret the probability. (minimum of 3 complete sentences) (#6) What is your advice to this military hero? (minimum of 3 complete sentences)

Explanation / Answer

here as z=(X-mean)/std deviation

1)hence P(X<L266)= P(Z<(266-266)/18)=P(Z<0)=0.5

2)P(Z>266)=P(Z>0)=0.5

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

4)P(X>315)=1-P(Z<2.7222)=1-0.9968=0.0032

5) for a random person to have pregnancy duration above 315 days has probability =0.0032 which is very unusual

6) There might be a chance to have an extra marital affair, which needs to be looked upon as well he needs to see if baby is Ok or not cause lengthy pregnancy period can cause health probloem in children

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