Answer:
0.682 is the probability that one newborn baby will have a weight within one standard deviation of the mean.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 8 pounds
Standard Deviation, σ = 0.6 pounds
We are given that the distribution of weights of full-term newborn babies is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(weight between 7.4 and 8.6 pounds)
[tex]P(7.4 \leq x \leq 8.6) = P(\displaystyle\frac{7.4 - 8}{0.6} \leq z \leq \displaystyle\frac{8.6-8}{0.6}) = P(-1 \leq z \leq 1)\\\\= P(z \leq 1) - P(z < -1)\\= 0.841 - 0.159 = 0.682 = 68.2\%[/tex]
[tex]P(7.4 \leq x \leq 8.6) = 6.82\%[/tex]
This could also be found with the empirical formula.
0.682 is the probability that one newborn baby will have a weight within 0.6 pounds of the mean.
