Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
Given that X follows a normal distribution with a mean of 75 and a standard deviation of 5.
To Determine: P(X>80)
Solution:
P(X>a)
[tex]P(X>a)=P(\frac{X-\mu}{\sigma}>\frac{a-\mu}{\sigma})[/tex]P(X>80)
[tex]\begin{gathered} P(X>80)=P(\frac{X-\mu}{\sigma}>\frac{80-\mu}{\sigma}) \\ \mu=75,\sigma=5 \end{gathered}[/tex][tex]P(X>80)=P(\frac{X-\mu}{\sigma}>\frac{80-75}{5})[/tex][tex]\begin{gathered} P(X>80)=P(Z>\frac{5}{5}) \\ P(X>80)=P(Z>1) \end{gathered}[/tex]We now go to the standard normal distribution table to look up P(Z>1) and for Z=1.00
We find that
[tex]P(Z<1)=0.8413[/tex]Note, however, that the table always gives the probability that Z is less than the specified value, i.e., it gives us P(Z<1)=0.8413
Therefore:
[tex]\begin{gathered} P(Z>1)=1-P(Z<1) \\ P(Z>1)=1-0.8413 \\ P(Z>1)=0.1587 \end{gathered}[/tex]In percentage
[tex]\begin{gathered} P(X>80)=1-P(Z<1)=0.1587 \\ In\text{ Percentage} \\ P(X>80)=0.1587\times\frac{100}{1}\text{ \%=15.87\%} \end{gathered}[/tex]Hence, P(X>80) = 15.87%
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
