Question

Assume that the duration of human pregnancies can be described by a normal model with mean 266 days and standard deviation 15 days. Complete parts​ a) through​ d) below.

​a) What percentage of pregnancies should last between 265 and 270 ​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 nothing​)=0.30 ​ (Round to one decimal place as​ needed.) ​

c) Suppose a certain obstetrician is currently providing prenatal care to 30 pregnant women. Let (y overbar) represent the mean length of their pregnancies. According to the central limit​ theorem, what is the mean and standard deviation ​SD(y overbar​) of the normal model of the distribution of the sample​ mean, (y overbar)​? The mean is nothing. ​SD(y overbar​)=    ​(Round to two decimal places as​ needed.) ​

d) What is the probability that the mean duration of these​ patients' pregnancies will be less than 264 ​days? ​P(y overbar less than 264​)equals nothing ​(Round to three decimal places as​ needed.)

Answer 1

Refer Standard normal table/Z-table to find the probability OR use excel formula "=NORM.S.DIST(-0.2667, TRUE)" & "=NORM.S.DIST(-0.0667, TRUE)" to find the probability.

Convert to the percentage (That is multiply by 100)

Round to one decimal places

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Refer Standard normal table/Z-table, Lookup for z-score corresponding to area 0.30 to the right of the normal curve OR use excel formula "=NORM.S.INV(1-0.30)" to find the z-score.

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Refer Standard normal table/Z-table to find the probability OR use excel formula "=NORM.S.DIST(-0.7303, TRUE)" to find the probability.

Round to three decimal places