Please try to show work so I can figure out how to do it, thank you! The length
ID: 3205615 • Letter: P
Question
Please try to show work so I can figure out how to do it, thank you!
The length of human pregnancies, from conception to birth, is on average u 266 days with a corresponding standard deviation of o 16 days. Enough data has been collected on pregnancy length that we know it follows an approximately normal distribution. Use this information to answer the questions below. You may find it helpful to draw diagrams. 1) P (Xi 2950? 2) P (Xi 2800 3) What is the probability that a woman's pregnancy will last between 222 and 258 days? 4) What is the probability that a woman's pregnancy will last more than 258 or less than 222 days? 5) How would your answer to 4) change if the standard deviation for pregnancy length were greater than 16 days?Explanation / Answer
1) P(X>295) = P(Z> 295-266 / 16) =P(Z>1.8125) = 1-.9650 = .0350
2) P(X<280) = P(Z< 280-266/ 16) = P(Z< .875) = .8078
3) P( 222<X<258) = P( -2.75<Z<-.5) =(1-.003)-.3085 = .6885
4) P(222<X and X>258) = 1-.3085+.003 = .6945
5)It will becomes more as higer stdev means Z scores more towards the mean. Whihc means that the area outside these Z limits will he higher
6) Limits of 95 percentile: 266 +/- 1.96*16
7) The range of 95% interval will becomes smaller
8) From Z tables that' Z=-.84. So, 266-.84*16 = 252.56
9) A Z of -2.05 or 266-2.05*16 = 233.2
10) A Z of +2.05 or 266+2.05*16 = 298.8