29, According to Sciencedaily com, deliver within 10 days if their projected due

Question

29, According to Sciencedaily com, deliver within 10 days if their projected due dates. Researchers in the USA have been able to pinpoint the precise point at which a woman ovulates and a fertilised embryo implants in the womb during a naturally conceived pregnancy, and follow the pregnancy through to delivery. Using this information, they have been able to calculate the length of 125 pregnancies. the average gestational period for humans is 280 days but only 70% of women "We found that the average time from ovulation to birth was 268 days -98 weeks and tuo days," said Dr Anne Marie Jukic, a postdoctoral fellow in the Epidemiology Branch at the National Institute of Enuironmental Health Sciences (Durham, USA), part of the National Institutes for Health. "However, even after we had ercluded sir pre-term births, we found that the length of the pregnancies varied by as much as 37 days. Assume gestational period has a normal distribution. (a) Based on the average of 280 days and the statement that 70% deliver within 10 days, what is your best estimate for the standard deviation? (b) What is your best estimate, based on the new information provided by the researchers (average of 268 days varying as much as 37 days), for the standard deviation? (c) Find the 95th percentile for both scenarios.

Explanation / Answer

a)
z * sd = 10
z for 70 % confidence level = =NORMSINV(0.85) = 1.036433

1.036433 * sd = 10
sd = 10 /1.036433 = 9.6484

b)
95 % of data lies within 2 sd

2* sd = 37
sd = 37/2 = 18.5

c)
95th percentile = mean + z *sd
z for 95 % percentile = 1.645

for a) 280+9.6484*1.645=295.871618
b)268+1.645*18.5=298.4325

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