according to the central limittheorem, whats the distribution of this sample mean, y bar?

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assume that the duration od human pregnancies can be described by a normal model with a mean 266 days and standard deviation 16 days. suppose a certain obstetrician is currently providing prenatal care to 60 pregnant women. let y bar represent the mean length of their pregnancies.

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The number of women are = n =60

normal model with mean =266 days

standard deviation =16 days

The central limit theorem shows that y bar represent the mean length with normal distribution with mean of y and standard deviation of y bar is equal to standard deviation of y divided by square root of n

X bar ~ N.D( μ = 266 , σ = 16/sqrt60)

X bar ~ N.D( μ = 266 , σ = 2.065)

The distribution of this sample with mean 266 and standard deviation is 2.065

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