The probability that the mean weight of the sample babies would be less than 3631 grams is 0.1591 or 15.91%.
The mean weight of the babies (μ) = 3685 grams.
The variance (σ²) = 330625.
Therefore, the standard deviation (σ) = √330625 = 575.
The sample size (n) = 113.
The sample mean = μ - 3685 grams.
The sample standard deviation (s) = σ/√n = 575/√113 = 54.09145.
We are asked to find the probability that the mean weight of the sample babies is less than 3631 grams, that is,
P(X < 3631) = P(Z < {(3631 - 3685)/54.09145})
Using the formula: Z = (x - μ)/s,
or, P(Z < -0.9983) = 0.1591 or 15.91%.
From the table of area under the z-score.
P(X < 3631) can also be calculated using calculator function:
Normalcdf(-100000000,3631,3685,54.0195), which gives the value 0.1591 or 15.91%.
Thus, the probability that the mean weight of the sample babies would be less than 3631 grams is 0.1591 or 15.91%.
Learn more about the probability of sampling distributions at
https://brainly.com/question/15291567
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