The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of 5 minutes and a standard deviation of 2 minutes. Find the probability that it takes at least 8 minutes to find a parking space. (Round your answer to four decimal places.)
Accepted Solution
A:
Answer: 0.0668Step-by-step explanation:Given: Mean : [tex]\mu = 5\text{ minutes}[/tex]Standard deviation : [tex]\sigma = 2\text{ minutes}[/tex]The formula to calculate z is given by :-[tex]z=\dfrac{X-\mu}{\sigma}[/tex]To check the probability it takes at least 8 minutes (X≥ 8) to find a parking space. Put X= 8 minutes[tex]z=\dfrac{8-5}{2}=1.5[/tex]The P Value =[tex]P(z\geq1.5)=1-P(z\leq1.5)=1- 0.9331927=0.0668073\approx0.0668[/tex]Hence, the probability that it takes at least 8 minutes to find a parking space = 0.0668