Question

Question 7 0 out of 0.66667 points Find the area under the normal curve with mean 45 and standard deviation 3.5 to the right of x148 Round to four decimal places. Selected Answer: [None Given Response To find the area to the right of an x-value, use the Normalodt function on your calculator. You are given the lower bound, and you can either type in Feedback: 1E99 to represent infinity, or you can use a very large number like 100,000. Use the mean and standard deviation given instead of 0 and 1 Question 8 0 out of 0.66667 points Find the area under the normal curve with mean 45 and standard deviation 3.5 between x 42.1 and x 50.3. Round to four decimal places. Selected Answer: [None Given Response To find the area to the between x-values, use the Normalcdt function on your calculator. You are given the lower and upper bounds. Use the Feedback: mean and standard deviation given instead of O and 1

Answer 1

$\mathbf{Solution}$

$\mathbf{given:}\;mean\;(\mu)=45,\;standard\;deviation\;(\sigma)=3.5$

$\mathbf{formula:}\;z=\frac{x-\mu}{\sigma}$

${\color{blue} \mathbf{Question\;7}}$

$P(x>48)\Rightarrow P\left ( \frac{x-\mu}{\sigma}>\frac{48-45}{3.5} \right )$

$=P(z>0.86)$

$=\mathbf{{\color{Red} 0.1957}}\;(from\;z-table)$

${\color{blue} \mathbf{Question\;8}}$

$P(42.1<x<50.3)\Rightarrow P\left ( \frac{42.1-45}{3.5}<\frac{x-\mu}{\sigma}<\frac{50.3-45}{3.5} \right )$

$=P(-0.83<z<1.51)$

$=P(z<1.51)-P(z<-0.83)$

$=0.9350-0.2037\;(from\;z-table)$

$=\mathbf{{\color{Red} 0.7313}}$