Question

suppose the birth weights of full - term babies are normally distributed with mean 3750 grams and standard deviation (sigma = 475) grams. complete parts (a) through (c) below
(a) draw a normal curve with the parameters labeled. choose the correct graph below

Explanation:

Step1: Recall the properties of normal curve

The normal curve is symmetric about the mean. The mean of the distribution is \(\mu = 3750\) grams. Also, we can find the values one standard deviation away from the mean: \(\mu-\sigma=3750 - 475=3275\) and \(\mu+\sigma=3750 + 475 = 4225\)

Step2: Analyze each option

• Option A: The mean value labeled as \(3750\) is incorrect in terms of the one - standard - deviation values. \(2800\) is not \(\mu-\sigma\) (since \(\mu-\sigma = 3275\))
• Option B: The mean \(\mu = 3750\) is at the center of the curve. The values \(3275=\mu - \sigma\) and \(4225=\mu+\sigma\) are correctly placed one standard deviation away from the mean.
• Option C: The mean value is not \(3750\) (the center of the curve should be at \(3750\) not \(4225\) as the starting point for one - standard - deviation calculation from the center is wrong)
• Option D: The values \(2800\) and \(4700\) are not \(\mu\pm\sigma\) (since \(\mu-\sigma=3275\) and \(\mu+\sigma = 4225\))

Answer:

B.