Question

In the country of United States of Heightlandia, the height measurements of ten-year-old children areapproximately normally distributed with a mean of 56.7 inches, and standard deviation of 7.4 inches.What is the probability that the height of a randomly chosen child is between 58.2 and 72.6 inches? Do notround until you get your your final answer, and then round to 3 decimal places.Answer=(Round your answer to 3 decimal places.)Question Help: D Video

Answer 1

`\begin{gathered} \mu=56.7 \\ \sigma=7.4 \\ x1=58.2 \\ x2=72.6 \\ z=(x-\mu)/(\sigma) \\ z1=(58.2-56.7)/(7.4) \\ z1=0.203 \\ z2=2.15 \\ \text{for z1=0.203} \\ P(z1)=0.5910 \\ \text{for z2=2.15} \\ P(z2)=0.9842 \\ P(z2-z1)=0.9842-0.5910 \\ P(z2-z1)=0.3932\approx0.393 \\ \text{The probability that the height of a randomly chosen Child } \\ is\text{ betw}en\text{ 58.2 and 72.6 inches is 0.393} \end{gathered}`