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In: Statistics and Probability

Assume that the duration of human pregnancies can be described by a normal model with mean...

Assume that the duration of human pregnancies can be described by a normal model with mean 266 days and standard deviation 12 days. Complete parts​

​a) What percentage of pregnancies should last between 275 and 280 days? ​_________%

​(Round to one decimal place as​ needed.)​

b) At least how many days should the longest 30​% of all pregnancies​ last?

​P(X greater than or equals≥________​)=0.30

​(Round to one decimal place as​ needed.)​

c) Suppose a certain obstetrician is currently providing prenatal care to 90 pregnant women. Let y represent the mean length of their pregnancies. According to the central limit​ theorem, what is the mean and standard deviation SD(y overbary​) of the normal model of the distribution of the sample​ mean, y overbary​?

The mean is _________.

​SD(y overbary​)equals=__________

​(Round to two decimal places as​ needed.)​

d) What is the probability that the mean duration of these​ patients' pregnancies will be less than 265 days?

P(y overbaryless than<265​)equals=________

​(Round to three decimal places as​ needed.)

​(Round to three decimal places as​ needed.)

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