Math statistics

Question

If babies' weights are normally distributed with a mean of 3.23 kg and a standard deviation of 0.87 kg, find the range of weights that contain approximately

(a) 68% of the data

 kg --  kg

(b) 95% of the data

 kg --  kg 

(c) 99.7% of the data

 kg --  kg

Answer 1

You need to know the 68-95-99.7 Rule.

Approximately 68% of the data falls within 1 standard deviation of the mean of a normal distribution.

Approximately 95% of the data falls within 2 standard deviations of the mean of a normal distribution.

Approximately 99.7% of the data falls within 3 standard deviation of the mean of a normal distribution.

(a) 68% of the data: mean +/ se = 3.23 + / - 0.87 = (2.36 ,4.1)

(b) 95% of the data: mean +/ 2se = 3.23 + / - 2(0.87) = (1.49, 4.97)

(c) 99.7% of the data: mean +/ 3se = 3.23 + / - 3(0.87) = (0.62, 5.84)