ANSWER:
(a) 2.36 kg -- 4.1 kg
(b) 1.49 kg -- 4.97 kg
(c) 0.62 kg -- 5.84 kg
Explanation:
We can calculate the value in each corresponding interval by applying the following formula:
(a) For 68%:
![\begin{gathered} IQ=m\pm sd \\ m=\operatorname{mean} \\ sd=\text{standard deviation} \\ \text{ replacing:} \\ IQ=3.23\pm0.87 \\ IQ_1=3.23+0.87=4.1 \\ IQ_2=3.23-0.87=2.36 \\ \text{The range is (2.36, 4.1)} \end{gathered}]()
Thus, 68% of babies' weights have and IQ between 2.36 kg and 4.1 kg
(b) For 95%:
![\begin{gathered} IQ=m\pm2\cdot sd \\ m=\operatorname{mean} \\ sd=\text{standard deviation} \\ \text{ replacing:} \\ IQ=3.23\pm2\cdot0.87 \\ IQ_1=3.23+2\cdot0.87=4.97 \\ IQ_2=3.23-2\cdot0.87=1.49 \\ \text{The range is (1.49, 4.97)} \end{gathered}]()
Thus, 95% of babies' weights have and IQ between 1.49 kg and 4.97 kg
(c) For 99.7%:
![\begin{gathered} IQ=m\pm3\cdot sd \\ m=\operatorname{mean} \\ sd=\text{standard deviation} \\ \text{ replacing:} \\ IQ=3.23\pm3\cdot0.87 \\ IQ_1=3.23+3\cdot0.87=5.84 \\ IQ_2=3.23-3\cdot0.87=0.62 \\ \text{The range is (0.62, 5.84)} \end{gathered}]()
Thus, 99.7% of babies' weights have and IQ between 0.62 kg and 5.84 kg