Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

2. 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

2 If Babies Weights Are Normally Distributed With A Mean Of 323 Kg And A Standard Deviation Of 087 Kg Find The Range Of Weights That Contain Approximatelya 68 O class=

Sagot :

ANSWER:

(a) 2.36 kg -- 4.1 kg

(b) 1.49 kg -- 4.97 kg

(c) 0.62 kg -- 5.84 kg

STEP-BY-STEP EXPLANATION:

We can calculate the value in each corresponding interval by applying the following formula:

(a) For 68%:

[tex]\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}[/tex]

Thus, 68% of babies' weights have and IQ between 2.36 kg and 4.1 kg

(b) For 95%:

[tex]\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}[/tex]

Thus, 95% of babies' weights have and IQ between 1.49 kg and 4.97 kg

(c) For 99.7%:

[tex]\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}[/tex]

Thus, 99.7% of babies' weights have and IQ between 0.62 kg and 5.84 kg

Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.